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Full text of "Laboratory methods for sensory analysis of food"

Laboratory methods for 
sensory analysis of food 




Agriculture 
Canada 



Digitized by the Internet Archive 

in 2011 with funding from 

Agriculture and Agri-Food Canada - Agriculture et Agroalimentaire Canada 



http://www.archive.org/details/laboratorymethodOOotta 



Laboratory methods for 
sensory analysis of food 



Linda M. Poste, 1 Deborah A. Mackie, 1 
Gail Butler, 2 and Elizabeth Larmond 3 



1 Food Research Centre 
Agriculture Canada, Ottawa, Ontario 

2 Research Program Service 
Agriculture Canada, Ottawa, Ontario 

3 Grain Research Laboratory 

Canadian Grain Commission, Winnipeg, Manitoba 




Research Branch 
Agriculture Canada 
Publication 1864/E 
1991 



©Minister of Supply and Services Canada 1991 



Available in Canada through 

Associated Bookstores 

and other booksellers 

or by mail from 

Canada Communication Group— Publishing Centre 
Ottawa, Canada K1A 0S9 

Catalog No.A73-1864/1991E 
ISBN 0-660-13807-7 

This publication replaces Publication 1637 Laboratory methods for sensory 
evaluation of food 

Canadian Cataloguing in Publication Data 

Laboratory methods for sensory analysis of food 
Linda M. Poste ... [et al.l. 

(Publication ; 1864/E) 

Rev. ed. of: Laboratory methods for sensory 
evaluation of food / Elizabeth Larmond. 
Includes bibliographical references. 

Cat. no. A73-1864/1991E 
ISBN 0-660-13807-7 



I. Food-Sensory evaluation. I. Poste, Linda M. 

II. Canada. Agriculture Canada. III. Larmond, Elizabeth. 
Laboratory methods for sensory evaluation of food. 

IV Series: Publication (Canada. Agriculture Canada). 
English ; 1864/E. 

TP372.5L3 1991 664'.07 C91-099103-0 



Produced by Research Program Service 

Cette publication est disponible en franc,ais sous le titre 
Methodes d'analyse sensorielle des aliments en laboratoire 



Staff Editor: Jane T. Buckley 



11 



Contents 
Preface vi 

Acknowledgments vii 

Introduction 1 

Factors influencing sensory measurements 

Expectation error 2 

Stimulus error 2 

Logical error 2 

Leniency error 2 

Halo effect 3 

Suggestion effect 3 

Positional bias (order effect) 3 

Contrast effect and convergence error 3 

Proximity error 4 

Central tendency error 4 

Motivation 4 

Physical facilities 4 

Testing area 4 

Training area 8 

Preparation and serving area 8 

Sample preparation 9 

Dilution and carriers 10 

Serving temperature 10 

Utensils and containers 10 

Quantity of sample 11 

Number of samples 11 

Reference samples 11 

Coding 12 

Order of presentation 12 

Rinsing 12 

Information about sample 13 

Time of day 13 

Selection and training of panelists 13 

Selection criteria 13 

Health 14 

Interest 14 

Availability and punctuality 14 

Verbal skills 14 
Selection and screening 14 
Training 15 



in 



Experimental design 16 

Samples 16 
Hypotheses to test 16 
Size of experiment 17 
Blocking 17 
Randomization 18 

Statistical tests 18 

Sensory analysis test methods 19 

Discriminative tests 19 

Triangle test 20 
Duo-trio test 22 
Two-out-of-five test 23 
Paired comparison test 25 
Ranking test (Friedman) 26 

Descriptive tests 29 

Scaling methods 30 

Structured scaling 30 

Unstructured scaling 33 

Tukey's test 38 

Unstructured scaling with replication 39 

Dunnett's test 45 

Ratio scaling 46 
Descriptive analysis methods 52 

Flavor profiling 52 

Texture profiling 54 

Quantitative descriptive analysis 56 

Food Research Centre panel 57 

Affective tests 61 

Paired comparison preference test 62 
Hedonic scaling test 64 
Ranking test 67 

Sensory analysis report 69 

Title 69 

Abstract or summary 69 
Introduction 70 
Experimental method 70 
Results and discussion 71 
Conclusions 73 
References 73 

References 74 



IV 



Appendixes 77 

Statistical Chart 1 

Statistical Chart 2 

Statistical Chart 3 

Statistical Chart 4 

Statistical Chart 5 

Statistical Chart 6 

Statistical Chart 7 

Statistical Chart 8 

Statistical Chart 9 



Statistical Chart 10 
Statistical Chart 11 



Table of random numbers, 
permutations of nine 78 

Triangle test, probability chart, 
one-tailed 80 

Two-sample test, probability chart, 
two-tailed 81 

Two-sample test, probability chart, 
one-tailed 82 

Two-out-of-five test 83 

Chi square, x 2 > percentage points 84 

Significant studentized range at the 5% level 85 

Distribution of t 86 

Variance ratio— 5 percentage points for 
distribution of F 87 

Variance ratio— 1 percentage points for 
distribution of F 88 

Table oft for one-sided Dunnett's test 89 

Table oft for two-sided Dunnett's test 90 



Preface 



This revision of Laboratory methods for sensory evaluation of food has 
been updated throughout to include changes and advances that have 
occurred since the first edition was published in 1967 and revised in 1977. 

Because of continued demand for the publication, especially as a 
teaching aid and for use in small companies with limited technical 
expertise, an updated version was felt to be necessary. 

Three dedicated young scientists who now lead the sensory analysis 
team at Agriculture Canada, Ottawa, have made significant contributions 
in the updating and revision. It has been a pleasure to work with them and 
to pass on the gauntlet to a new generation. 

This edition is still intended as a manual and is prescriptive in nature. 
Readers are referred to some of the excellent texts that deal with the 
principles underlying the practices recommended here. 

Elizabeth Larmond 



VI 



Acknowledgments 



The authors thank John Wiley and Sons, Inc., for permission to reprint in 
part the Tables of random permutations (Statistical Chart 1) from 
Experimental designs by William G. Cochran and Gertrude M. Cox, 1957. 
We would also like to thank the Institute of Food Technologists for 
permission to reprint statistical charts 2, 3, and 4 from the Journal of Food 
Science 43(3):942-943 by E.B. Roessler, R.M. Pangborn, J.L. Sidel, and H. 
Stone (copyright by the Institute of Food Technologists). We acknowledge 
with thanks CRC Press Inc. for permission to reprint Table T5 (Statistical 
Chart 6) from Sensory analysis techniques, Volume II by M. Meilgaard, G. 
Vance Civille, and Thomas B. Carr, 1987. We thank Iowa State University 
Press, Ames, Iowa, for permission to reprint statistical charts 7 and 8 from 
Statistical methods by George W. Snedecor and William G. Cochran, 8th 
edition, 1989. We are also grateful to the literary executor of the late Sir 
Ronald A. Fisher, FRS, Cambridge, Dr. Frank Yates, FRS, Rothamstead, 
and Messrs. Oliver and Boyd Ltd., Edinburgh, for permission to reprint in 
part Table V (Statistical Chart 9) from their book Statistical tables for 
biological, agricultural, and medical research (6th edition 1974). The 
authors also thank the Biometric Society for permission to reproduce 
statistical charts 10 and 11. We also wish to thank Diversified Research 
Laboratories Limited, Toronto, for permission to use a photograph of their 
facilities (Fig. 1). We owe a special debt of gratitude to everyone who has 
advised and worked with us in preparing this book and Drs. J.J. Powers, 
M. McDaniel, and B.K. Thompson for their reviews. Finally, our most 
sincere thanks and gratitude go to Mrs. Josiane Obas for her dedicated 
efforts in typing our manuscript. 



vn 



Introduction 



Sensory evaluation was defined by the Sensory Evaluation Division of the 
Institute of Food Technologists (1975) as "the scientific discipline used to 
evoke, measure, analyze and interpret those reactions to characteristics of 
foods and materials as perceived through the senses of sight, smell, taste, 
touch and hearing." The complex sensation that results from the 
interaction of our senses is used to measure food quality in programs such 
as quality control and new product development. This evaluation may be 
carried out by panels of a small number of people or by several hundred 
depending on the type of information required. 

The first and simplest form of sensory analysis is made at the bench by 
the research worker who develops the new food products or quality control 
specifications. Researchers rely on their own evaluation to determine gross 
differences in products. Sensory analysis is conducted in a more formal 
manner by laboratory and consumer panels. 

Most sensory characteristics of food can only be measured well, 
completely, and meaningfully by human subjects. Advances continue to be 
made in developing instrumental tests that measure individual quality 
factors. As instruments are developed to measure these factors, sensory 
analysis data are correlated with the results to determine their predictive 
ability. 

When people are used as a measuring instrument, it is necessary to 
control all testing methods and conditions rigidly to overcome errors 
caused by psychological factors. "Error" is not synonymous with mistakes 
but may include all kinds of extraneous influences. The physical and mental 
condition of the panelists and the influence of the testing environment 
affect their sensory responses. 

Sensory analysis panels can be grouped into four types: highly trained 
experts, trained laboratory panels, laboratory acceptance panels, and large 
consumer panels. 

Highly trained experts (1-3 people) evaluate quality with a very high 
degree of acuity and reproducibility, e.g., wine, tea, and coffee experts. 
Evaluations by experts and trained laboratory panels can be useful for 
control purposes, for guiding product development and improvement, and 
for evaluating quality. The trained panel (10-20 people) can be particularly 
useful in assessing product attribute changes for which there is no adequate 
instrumentation. Sensory analyses performed by laboratory acceptance 
panels (25-50 people) are valuable in predicting consumer reactions to a 
product. Large consumer panels (more than 100 people) are used to 
determine consumer reaction to a product. 



Factors influencing sensory measurements 



Standard procedures for planning and conducting sensory panels have 
been developed in an effort to minimize or control the effect that 
psychological errors and physical conditions can have on human judgment. 
The need for standardized procedures can perhaps be emphasized by 
describing some of the factors that affect human judgment and by outlining 
ways in which to minimize or eliminate them. 

Expectation error 

Any information that panelists receive about the test can influence the 
results. Panelists usually find what they expect to find. Therefore, give 
panelists only enough information for them to conduct the test. Do not 
include on the panel those persons who are directly involved with the 
experiment. Code the samples so that the panelists cannot identify them, 
as the code itself should introduce no bias. Because people generally 
associate "1" or "A" with "best," we recommend the use of three-digit 
random numbers. 



Stimulus error 

In a desire to be right, the judgment of the panel members may be 
influenced by irrelevant characteristics of the samples. For example, when 
asked if there is a difference in the sweetness of two samples of peach 
halves, a panelist may look for help in every possible way such as the 
following: Are the pieces of uniform size? Is there a difference in color? Is 
one firmer than the other? Because of this stimulus error, make all samples 
as uniform as possible. If unwanted differences occur between samples, 
mask them whenever possible. 

Logical error 

Closely associated with stimulus error is logical error, which can cause the 
panelist to assign ratings to particular characteristics because they appear 
to be logically associated with other characteristics. A slight yellow color in 
dehydrated potatoes, for example, might indicate oxidation to the panelist 
who could logically find a different flavor in the sample. Control this error 
by keeping the samples uniform and masking differences. 

Leniency error 

This error occurs when panelists rate products based on their feelings 
about the researcher, in effect ignoring product differences. Therefore, 
conduct tests in a controlled, professional manner. 



Halo effect 

Evaluating more than one factor in a sample may produce a halo effect. The 
panelist often forms a general impression of a product and if asked to 
evaluate it for odor, texture, color, and taste at the same time, the results 
may differ from those when each factor is rated individually. In effect, the 
rating of one factor influences the rating of another. For example, in meat 
evaluations, often panelists will rate a dry sample tougher than it would be 
if tenderness alone were being assessed. When resources allow, eliminate 
this effect by evaluating only one characteristic at a time. 

Suggestion effect 

Reactions of other members of the panel can influence the response of a 
panelist. For this reason, separate panelists from each other in individual 
booths. Do not permit them to talk during the testing so that a suggestion 
from one panelist will not influence another. Keep the testing area free 
from noise and distraction, and separate from the preparation area. 



Positional bias (order effect) 

Often panelists score the second product (of a set of products) higher or 
lower than expected regardless of the product because of position effect. In 
some tests, particularly the triangle test, a positional bias has been shown. 
When there are no real sample differences, panelists generally choose the 
middle sample as being different. Avoid this error by making either a 
balanced or a random presentation of samples. In a small experiment, use a 
balanced presentation to ensure every possible order is presented an equal 
number of times. In a large experiment, randomize the samples. 

Contrast effect and convergence error 

A contrast effect occurs between two products that are markedly different; 
panelists will commonly exaggerate the difference in their scores. For 
example, presenting a sample that is very sweet before one that is slightly 
sweet causes the panelist to rate the second sample lower in sweetness than 
it would normally be rated; the reverse is also true. 

Convergence error is the opposite of contrast effect. A large difference 
between two (or more) products may mask small differences between other 
samples in the test causing scores to converge. To correct for both these 
errors, randomize the order of presentation of the samples for each 
panelist, so as to equalize these effects. 



Proximity error 

When a set of samples are being rated on several characteristics, panelists 
usually rate more similar those characteristics that follow one another (in 
close proximity) on the ballot sheet than those that are either farther apart 
or rated alone. Thus, the correlations between characteristics close 
together may be higher than if they were separated by other 
characteristics. Minimize this error either by randomizing the 
characteristics on the ballot sheet or by rating only one characteristic at a 
time. 



Central tendency error 

This error is characterized by panelists scoring products in the midrange of 
a scale to avoid extremes. It causes the treatments to appear more similar 
than they may actually be and is more likely to occur if panelists are 
unfamiliar with either the products or the test method. To minimize this 
error, balance or randomize the order of presentation as this effect is more 
noticeable for the first sample. Train panelists to familiarize them with the 
test method and products. 

Motivation 

The motivation of the panelists affects their sensory perception. An 
interested panelist is always more efficient and reliable and is essential for 
learning and good performance. Maintain the interest of each panelist by 
giving them reports of their results. Trained panelists are generally more 
motivated than those who are not trained (Ellis 1961). Help to make 
participants feel that the panels are an important activity by running the 
tests in a controlled, efficient manner. 



Physical facilities 



Testing area 



Sensory analysis requires a special testing area that is kept constant 
throughout all tests and where distractions are minimized and conditions 
are controlled (Fig. 1). In designing an area, consider management support, 
location, space requirements, environmental aspects, construction, cost, 
and laboratory design (American Society for Testing and Materials 1986). 
Each type of testing, for example, discriminative and descriptive testing, 
focus group, or consumer panel testing, demands some modification to the 
design of the facilities. The testing environment should provide a quiet, 
comfortable environment complete with an air conditioner and source of 
heat to maintain 22 °C. A controlled humidity of 44-45% RH may be 



required for testing some products (American Society for Testing and 
Materials 1986). 

Most types of testing, excluding profile methods, require independent 
responses from the panelists. To accomplish this, provide the testing area 
with individual booths that are adjacent to a separate sample preparation 
and serving area. The booths may be as simple as partitions either put on a 
table or hinged to collapse when the laboratory bench is used for other 
purposes. American Society for Testing and Materials (ASTM) (1986) has 
recommended a booth width of between 70 and 80 cm, a depth of between 
45 and 55 cm, and a countertop height of 75 cm (Fig. 2). The usual method is 
to construct booths along the wall that divides the testing area from the 
preparation area. If both countertops (preparation and testing area) are at 
the same height, the product can be passed through from the preparation 
area to the panelists. The pass-through can be either a sliding door or a 
bread-box style (Fig. 3). Construct all walls and booths of opaque, 
nonreflecting material, which is neutral in color (off-white, white, light 
gray), easily cleaned, and ideally divided by dividers that extend out 40 cm 
beyond the countertop. Panelists should not enter the preparation area, as 
they might gain information about the sample that may influence their 
responses. 

The booth may be fairly simple or very elaborate depending on the 
funds available, the type of products being tested, and the types of tests or 
panels required. Many laboratories have a sink and tap built into each 
booth for expectoration and to provide water for rinsing. We do not 
recommend sinks for food and beverage testing because, if they are not 




Fig. 1 Sensory analysis area. (Diversified Research Laboratories Ltd.) 



properly maintained, sanitation and odor problems will result (Ellis 1961). 
Noise is sometimes also a problem. Sinks are often required for testing 
personal care products and, if so, we recommend a suction type, such as 
dentists use. A tap for rinsing water in the booth is undesirable because it is 
difficult to control the temperature of the water. It is generally advisable to 
pour the water well before the test so that it will be at room temperature. 
Water can be tap, bottled spring, or distilled. Some testing requires such 
items as mirrors, electrical outlets, or hot plates. 

Develop some method of communication from the panelist to the 
researcher. In some laboratories, a switch in each booth connected to lights 
in the preparation area acts as the signal that a panelist is ready for the 
samples. Other methods are the placement of a tag with the panelist's 
name on it into the pass-through or a direct data entry system whereby the 
panelist logs in on a computer terminal. 




Fig. 2 Panelist with samples and questionnaire. 



Ensure that lighting is uniform and does not influence the appearance 
of the product being tested. Choose carefully the type of light used if color 
and appearance are important factors to be judged. The American Society 
for Testing and Materials (1986) has recommended incandescent and 
fluorescent lighting, which will provide a variety of intensities ranging from 
about 753 lux to at most 1184 lux. Install a dimmer switch to create varying 
intensities of light. The International Organization for Standardization 
(ISO) (1985) has recommended lights having a correlated color 
temperature of 5000/6500 K. To eliminate differences in color between 
samples, colored lights are sometimes used; the most common are red, 
green, or blue. These lights have not been particularly effective because 
differences in the hue or depth of color are still noticeable. Amerine et al. 
(1965) pointed out that it is not known what effect colored or dim lighting 
has on judgment. It may have less effect on experienced panelists who are 
accustomed to it, but inexperienced panelists have expressed a dislike for 
testing under colored lights. In the laboratory at the Food Research Centre, 
we have had panelists experience a claustrophobic feeling upon entering a 
room lit with colored lights. Any evaluations made under this type of stress 
would be questionable. Sodium lighting is another alternative for masking 
color differences. 

Keep foreign odors and odors from the food preparation area from the 
testing room. Do not allow smoking in this area at any time. Panelists 
should also avoid cosmetics. The American Society for Testing and 
Materials Committee E-18 on Sensory Evaluation of Materials and 
Products (1986) has recommended that a slight positive pressure 




Fig. 3 Presentation of sample through bread-box-style hatch. 



maintained in the testing area prevents odors entering from surrounding 
areas. That committee also recommended the use of activated charcoal 
filters in the incoming air vents for an odor-free area; these filters need to 
be changed or reactivated at intervals. 

Training area 

Provide an area for training a profile or descriptive analysis panel (Fig. 4). 
Ideally, the area would be separate and adjacent to the preparation area, if 
space allows. Often it is part of the booth area. A round table, large enough 
for 6-12 panelists, allows discussion among the trainees. A table that has a 
movable centre or lazy susan for passing standards or reference samples 
back and forth is very useful. Ensure that the lighting and ventilation are 
similar to that described for the booth area and that tables, chairs, 
floorings, and walls are neutral in color, nonodorous, and easily cleaned. To 
facilitate discussion, provide a blackboard, whiteboard, or flip chart, but be 
aware of the odor given off by some markers. Lastly, include a clock to 
ensure that the panel leader does not exceed the allotted training time. 







Fig. 4 Training area. 



i 



Preparation and serving area 

The type of preparation area and equipment will depend on the type of 
products being tested. A well-equipped kitchen is a good start, with 
specialized equipment being added according to need. Install in the 
preparation area a good ventilation system to remove odors and an air 



8 



conditioner to maintain a controlled temperature. We cannot 
overemphasize the need for sufficient counter space for serving and 
assembling samples for presentation and cabinet space for storage. Within 
the preparation area, provide refrigerated and frozen storage space to 
store or hold samples. Arrange for extra refrigerated and frozen storage, 
for larger volume storage, in another location if needed. If heating or 
cooking of samples is necessary, then install equipment such as electric or 
gas burners (the burners must be the same size) and ovens (e.g., 
conventional, convection, or microwave). Other equipment may include 
water baths, heating trays, incubators, meat cutters, balances, heat lamps, 
scales, mixers, bottled water dispensers, and fire extinguishers. For 
cleaning purposes the preparation area may include dishwashers, garbage 
disposers, trash compactors, in addition to the required waste baskets, 
sinks, and water sources. When considering equipment, address such 
factors as initial cost, quality, service availability, space and installation 
requirements, cleanability, noise level, and odor generation. When 
selecting materials for the construction of the preparation area, keep the 
colors neutral and avoid reflective materials such as glass and mirrors, 
which are difficult to keep clean. Vinyl coverings and tiles are suitable for 
walls and floors and plastic laminates for cupboards and countertops. 
Consider having a telephone in the preparation area for contacting 
panelists who are late for a panel. But we do not recommend installing a 
telephone in the booth area, because it is distracting if it rings. 



Sample preparation 



Preliminary testing is usually needed to decide on the method of 
preparation; thawing, preparation, and cooking time; and equipment and 
utensils. For difference (discriminative) testing, select the preparation 
method that is unlikely to mask, add to, or alter the basic characteristics of 
the product. For affective testing, prepare the product using a method 
typical of, or that represents, the way in which it is actually prepared and 
consumed. 

Once a method has been chosen, keep it constant throughout tests on 
the product. The preparation method must not impart any foreign tastes or 
odors to the product. Samples should represent or be typical of the product 
or material to be tested. Except for the factor (or factors) under study, 
prepare all samples tested at a given time or in a given experiment and 
serve them using exactly the same procedures. 

Panelists are influenced by irrelevant characteristics of the samples. 
Therefore, make every effort to prepare samples from different treatments 
identically to remove any irrelevant differences. To achieve this, it may be 
necessary to cut, dice, grind, or puree the samples to obtain uniformity of 
sample presentation across treatments. 

When conducting affective tests, it is better to present one sample at a 
time rather than grind or puree the product to mask differences. Color 



differences are sometimes masked by colored or dimmed lights, as 
previously discussed. The use of colored containers such as ruby-red 
glasses or black-lined cups masks color differences. Dyes that impart no 
flavors have also been used to eliminate color differences. 



Dilution and carriers 

Some products, by their very nature, need either to be diluted or to be 
served with a carrier. For example, hot sauces, flavorings, spices, and 
sauces usually require dilution prior to testing. Spices can be mixed into a 
bland white sauce or syrup, but do consider the effect of the sauce or syrup 
on the flavor. For example, several researchers have shown that 
hydrocolloid gels have flavor-masking effects (Marshall and Vaisey 1972; 
Pangborn and Szczesniak 1974). 

Some products, such as whipped topping, cheese spread, and ketchup, 
do not require carriers (Kroll and Pilgrim 1961). In their study, they found 
that discrimination was better without a carrier in some cases. The use of a 
carrier, such as crackers for jam or frankfurters for ketchup, adds to the 
cost and effort, and it is often difficult to select an appropriate carrier. 
Carriers are also a source of experimental error because either the 
proportion of product to carrier may not be constant, or the carrier may 
not be of consistent quality. 

The nature of a product may sometimes require that it be tested with a 
carrier during some of the testing. Test pie filling with pastry to see how the 
two interact, especially in terms of texture. Test icing on cake not only to 
examine flavor combinations, but also to see how the icing handles. 

Serving temperature 

The temperature at which samples are served can cause many problems. 
For affective tests, serve the samples at the temperature at which they are 
normally consumed. 

However, in discriminative or descriptive tests, modify the 
temperature to account for the fact that taste acuity or perception is 
considered to be greatest at a temperature between 20° and 40 °C. The 
temperature throughout the experiment must remain constant for the 
results to be comparable. To achieve this, use warming ovens with a 
controlled thermostat, water baths, styrofoam cups, heated sand, 
doubleboilers, or wrap in foil. If the samples are to be held for any length of 
time, take care that they do not dry out or change in quality during holding. 
For example, do not cut meat samples until ready to serve; otherwise they 
will dry out, which will affect the sensory rating. 

Utensils and containers 

Serving utensils should impart neither taste nor odor to the product. Use 
identical containers for each sample so that no bias will be introduced from 



10 



this source. Unless differences in color are being masked, it is wise to use 
colorless or white containers. Consider factors such as ease of coding, type 
of product, and serving temperature when you select containers. 
Disposable dishes made from hard plastic, unwaxed paper, or styrofoam 
are convenient when large numbers are to be served. Determine 
beforehand that no taste is transferred to the product. Glass is an excellent 
vessel; however, it requires time spent in washing and rinsing to ensure that 
no flavor or odor is left from the products or soap used. Breakage of glass is 
also a problem. 

Quantity of sample 

The amount and size of sample given to each panelist is often limited by the 
quantity of experimental material available. The sample, even if small, 
should be representative of the product. Even when using a small amount 
of sample, each panelist must have enough to assess the product and 
retaste, if necessary. Make the amount of sample presented constant 
throughout the testing. When using a reference sample, we recommend 
that you present twice as much sample as the experimental sample to allow 
panelists to keep referring back to the reference. 

The Committee E-18 of the American Society for Testing and 
Materials (1968) has recommended that, in discriminative tests, each 
panelist should receive at least 16 mL of a liquid and 28 g of a solid, and that 
the amount should be doubled for preference tests. In some tests, panelists 
have been asked to consume a normal serving size of a product. For 
example, during acceptability studies on flavored milk, panelists were 
asked to drink 190 mL of the product before rating the acceptability. Such a 
product might be very pleasing when you drink 30 mL, but if you drink 190 
mL you might find it too sweet or satiating. 

Number of samples 

With input from panelists, in preliminary work, determine the number of 
samples that can be effectively evaluated in one session. Consider not only 
the type of product, the number of characteristics to be evaluated, the type 
of test, and the experience of the panel, but also the motivation of the 
panelists. The number of samples that can be presented in a given session is 
a function of both sensory and mental fatigue in the panelist (Meilgaard et 
al. 1987a). 



Reference samples 

Inclusion of a known (or marked) reference sample (or samples) may assist 
panelists in their responses and may decrease the variation in judgment. 
For example, if you cannot present all the samples at once, the use of a 
reference sample may be helpful. The reference sample must be the same 
each day of evaluation throughout the experiment and can be anchored to 



11 



the scales. A reference sample included as a coded sample provides a check 
on a panelist's consistency in evaluations. 

Coding 

The code assigned to the samples should give the panelists no hint of the 
identity of the treatments, and the code itself should not introduce any 
bias. We recommend three-digit random numbers obtained from tables of 
random numbers for coding the samples. A table of random numbers is 
presented in Statistical Chart 1 (Appendix). Enter anywhere on the table 
and, by moving either horizontally or vertically, select three consecutive 
numbers. If replication is being done, the panelists are usually the same, 
therefore, a new set of codes is required for each replicate. Because some 
marking pens can leave an odor, use a wax pencil particularly for odor 
testing to mark containers with the number. Computer-generated labels 
can also be used. 



Order of presentation 

Many psychological and physiological effects, which we have discussed 
earlier, make it necessary to have an order of presentation that is either 
balanced or random. With a small number of samples and panelists, a 
balanced order makes it possible for every order to occur an equal number 
of times. In larger experiments, randomize the order using tables of 
random numbers or by computer using statistical software. To obtain a 
random order presentation, first assign a number to each treatment, e.g., 
sample A = 1, sample B = 2..., etc. Then, randomly enter the random 
number table (Statistical Chart 1) and determine the order of presentation 
as you come across each treatment number (horizontally or vertically). 

Rinsing 

Provide panelists with an agent for oral rinsing between samples. Many 
researchers prefer taste-neutral water at room temperature, but, when 
fatty foods are being tested, warm water, warm tea, lemon water, or a slice 
of apple or Japanese pear is a more effective cleansing agent. Unsalted 
crackers, celery, and bread have all been used for removing residual flavors 
from the mouth. Some researchers insist that the panelists rinse between 
each sample and others allow them to rinse or not according to personal 
preference. Whatever the case, each panelist should follow the same 
procedure consistently after each sample. In some cases, you may need to 
control the time between samples to prevent carryover from one sample to 
another, but panelists are usually allowed to work at their own speed. 



12 



Information about sample 

Give the panelists as little information as possible about the test to avoid 
influencing results. If they are given information about samples, panelists 
will have some pre-conceived impression of what to expect. Because this 
expectation error exists, do not include on the panel persons who are 
directly involved with the experiment. 

Time of day 

The time of day that tests are conducted influences the results (Amerine et 
al. 1965). Although time cannot always be controlled if the number of tests 
is large, late morning and mid afternoon are generally the best times for 
testing. 

Consider the type of product being sampled. Too early in the morning 
or afternoon is objectionable to some panelists, especially so if the foods 
served are hot, spicy ones. If it is too late in the day, some panelists may lack 
motivation. Avoid mealtimes. Set the schedule taking into consideration 
other testing to be done. 



Selection and training of panelists 



The panel is the analytical instrument in sensory analysis. The value of this 
tool depends on the objectivity, precision, and reproducibility of the 
judgment of the panel members. Before a panel can be used with 
confidence, the ability of the panelists to reproduce judgments must be 
determined. Panelists for descriptive testing need to be carefully selected 
and trained. 

Panelists for laboratory testing are usually office, plant, or research 
staff. It should be regarded as part of a normal work routine for personnel 
to participate on a panel; they should be expected to evaluate all products. 
However, do not ask any person to evaluate food to which they object or 
may have an allergic reaction. Management support and full cooperation of 
the supervisors of persons who serve as panelists are necessary. A small, 
highly trained panel will give more precise and consistent results than a 
large, untrained panel. 

Selection criteria 

Selection is essential to develop an effective descriptive sensory panel. 
Select panelists on the basis of certain personal characteristics and 
potential capability in performing specific sensory tasks. Include in the 
selection criteria health, interest, availability punctuality, and verbal skills. 



13 



Health 

Persons who serve as panelists should be in good health and should excuse 
themselves when suffering from conditions that might interfere with 
normal functions of taste and smell. For example, colds, allergies, 
medications, and pregnancy often affect taste and smell sensitivities. We 
recommend that panelists refrain from smoking, chewing gum, eating, or 
drinking for at least 30 min before testing. Keep records of panelists' 
allergies, likes, and dislikes. 

Interest 

Emotional factors, interest, and motivation appear to be more important 
than the age or sex of panelists. Motivation affects their response. Interest 
is essential for learning and good performance, but often it is difficult to 
maintain a panelist's interest. One solution could be to provide each with 
the test results. You can help panelists to feel that panels are an important 
activity and that their contribution is important by running the tests in a 
controlled, efficient manner. 

Availability and punctuality 

Availability of the panelist during training and testing is essential. Persons 
who travel frequently and some production personnel are unsuitable to 
serve on panels. Punctuality is essential not only to avoid wasting people's 
time but also to avoid loss of integrity in sample and experimental design. 
Encourage punctuality by providing advance notice of all tests, i.e., a test 
schedule, regularly scheduled test sessions, and a personal reminder or 
telephone call shortly before test sessions. 

Verbal skills 

The degree of verbal skills that is required of the panelist depends on the 
test methodology. Descriptive tests generally require good verbal 
communication skills because panelists are expected to define and describe 
various characteristics of products. 

Selection and screening 

Amerine et al. (1965) believed that by selecting and training panelists with 
consistent, discriminative abilities, panels could be small and efficient. 
Threshold tests are not useful in selecting panelists because sensitivity to 
the primary tastes may not be related to the ability to detect differences in 
food. A more realistic approach is to select panelists on their ability to 
detect differences in the food to be evaluated. Ideally you should screen two 
to three times as many people as you will need, using the product class that 
will be tested. Prepare the samples so the variation you obtain is similar to 



14 



that which the panel will find in the actual experiment. When possible, the 
test methods used for screening should be similar to the actual ones to be 
used during testing. Ensure that each person clearly understands each test 
method, score sheet, and evaluation technique. Rank each person 
according to their ability to differentiate among (for discriminative tests) 
or describe (for descriptive and profile tests) the samples prepared. The 
selected panelists should have inherent sensitivity to the characteristic 
being evaluated. Repeat the tests to get a measure of reproducibility. Select 
a new panel for each product. Persons who discriminate well on some 
products do not necessarily discriminate well on others. 

Discriminative tests include triangle, duo-trio, two-out-of-five, paired 
comparison, and ranking test methods. Screening for a discriminative 
panel requires either that you present a series of triangle tests to each 
panelist and calculate the percentage of correct identification of odd or 
different samples (American Society for Testing and Materials 1981); or 
that you perform a sequential screening analysis (American Meat Science 
Association 1978). 

Descriptive analysis includes flavor profile, texture profile, 
quantitative descriptive analysis, and attribute rating methods. For the 
purpose of screening for flavor analysis, for which essentials are flavor 
memory and ability to deal logically with flavor perceptions, American 
Society for Testing and Materials (1981) recommended certain tests 

• to determine the panelist's ability to differentiate the basic tastes at 
above-threshold levels 

• to determine the panelist's aptitude for identifying and describing 20 
different odorants 

• to test the panelist's ability to rank basic taste samples in order of 
increasing concentrations. 

If texture analysis is required, test panelists for their ability to rank 
samples within various texture scales, e.g., hardness, viscosity, and 
geometrical characteristics in increasing order of attribute intensity 
(American Meat Science Association 1978). 

Training 

Training improves an individual's sensitivity and memory to provide 
precise, consistent, and standardized sensory measurements that can be 
reproduced. For panelists to make objective decisions, they must be trained 
to disregard their personal preferences. Training involves the development 
of a vocabulary of descriptive terms. Each panelist must detect, recognize, 
and agree upon the exact connotation of each descriptive term. The use of 
specially prepared reference standards or competitor's products that 
demonstrate variation in specific descriptive terms can help panelists 
during training sessions become more consistent in their judgments. 
Discuss the evaluation techniques for odor, appearance, flavor, and texture 
and agree upon a common procedure. Panelists must also become familiar 



15 



with the test method. Training time (from weeks to months) is a function of 
the product, the test procedure, and the capability of the panelists. 



Experimental design 



In planning experiments consider carefully the hypotheses to be tested, 
size of experiment, replication, blocking, randomization, and statistical 
tests. 



Samples 

Samples are taken to learn about the population being studied. The 
population is the total of all possible observations of the same product from 
which a sample is drawn. Characteristics will vary from sample to sample 
within a population. Therefore, when decisions about a population are 
based on samples, it is necessary to make allowance for the role of chance. 
Ensure that the samples fully represent the population from which they are 
drawn. 



Hypotheses to test 

Before selecting the test, the sensory analyst must establish the objective 
of the study, which is then stated in the form of a null hypothesis. For 
example, when testing two products having different levels of sweetener to 
see if the difference in sweetness is detectable, the null hypotheses might be 
as follows: "There is no difference in sweetness between these products." 

Based on the results of the statistical analysis of the experimental data, 
we either accept or reject the null hypothesis. Associated with the decision 
to accept or reject the null hypothesis are two types of error. A Type I error 
occurs when the null hypothesis is rejected when it is true; that is, saying 
there is a difference when in fact there is none. A Type II error occurs when 
the null hypothesis is accepted when in fact it is false; in other words, saying 
there is no difference when there really is one. 

The probability of making a Type I error is the level of significance (a). 
Usually the level of significance is set at 0.05 (5%) or 0.01 (1%). The 0.05 
level of significance means there is 1 chance out of 20 of saying there is a 
difference when there is no difference. A result is considered to be 
significant if the probability (P) is 0.05 or less. The probability of making a 
Type II error is (3. 

When working in research, statistical tests are usually set up to find 
differences. Therefore, Type I errors should concern us, namely, that we 
reject the null hypothesis when we should not reject it. However, often in 
sensory analysis, for quality assurance purposes, new products are tested 
against standard products to ensure that they do not differ. In this instance, 
the Type II error should concern us, namely, that we say there is no 



16 



difference when there really is a difference. If the latter occurs, consumers 
would notice the change when the new product is marketed and would 
possibly stop purchasing it. Therefore, we must minimize (3 by using acute, 
reliable panelists and by increasing the sample size (Larmond 1981). We 
refer the reader to O'Mahony (1986) for further discussion. 

Size of experiment 

The number of judgments collected will influence the statistical 
significance of the results. If too few judgments are obtained, large 
differences are required for statistical significance, whereas with a large 
number of judgments, statistical significance may result when differences 
are very small. Although statistical significance is important when 
reporting results, the size of the differences is also important. For example, 
a difference of 0.3 cm on a 15-cm line is unlikely to be meaningful (Larmond 
1981). If prior information on variability is available, an appropriate 
sample size can be estimated, which will result in those meaningful 
differences that do exist being statistically significant; see, for example, 
Steel and Torrie (1980) or Gacula and Singh (1984). If no information is 
available on variability, a preliminary study could provide this. 

Replication is necessary to provide an estimate of experimental error. 
Ideally, the sensory analyst should ensure that the replicates are 
independent units that represent the population. For example, if different 
varieties of applesauce were being evaluated, each panelist should receive 
applesauce from different tins (independent), rather than from the same 
tin. In some cases this design is not practical. For example, if roasts from 
different breeds of animals were being evaluated, several panelists might 
evaluate samples from the same roast (subsamples). The experimental unit 
in this case is the roast, not each panelist's sample, and we should compare 
the effect of breed to the among- roast variability. For further discussion of 
this aspect of design, see chapter 12 of Meilgaard et al. (19876). 

Blocking 

It is generally possible to increase the power (ability to detect real 
differences) of an experiment by removing known sources of variability 
from the estimate of error. For example, panelists often use different parts 
of a scale when makingjudgments. We can remove this variability from the 
error by pairing or blocking observations. That is, each panelist evaluates 
all treatments. Make samples for each panelist as homogeneous as possible 
so that comparisons will be as precise as possible. 

Treatments compared at the same time by the same panelist (in one 
block) are generally more precisely compared than those judged by 
panelists on different occasions. This may cause severe design restrictions. 
Differences in large numbers of treatments will be more difficult to 
estimate precisely than differences in a small number of treatments that a 
panelist can compare in one sitting. Further, because of the number of 



17 



treatments being considered or some particular characteristic of the 
product, such as a lingering aftertaste, it is not always possible to evaluate 
all treatments in one sitting. In these instances, an incomplete block design 
is used. Choose the most efficient design (smallest variance) possible. More 
replications are required to obtain the same efficiency as with a complete 
block design. When all treatments cannot be compared in one sitting, 
include controls, if possible, to improve comparability across sessions 
(Gacula 1978). For further details on complex designs, we suggest that you 
consult a statistician. This subject is discussed in more detail in Cochran 
and Cox (1957), Moskowitz (19886), Meilgaard et al. (19876), and Gacula 
and Singh (1984). 

Randomization 

Proper randomization is essential for valid, unbiased results. To guard 
against a treatment unknowingly being favored or disfavored throughout 
an experiment and to ensure an unbiased estimate of error, it is important 
to randomize. Items to be randomized include, for example, the order of 
presentation, the oven used in preparation, and the assignment of material 
to a treatment. The random number tables (presented as Statistical 
Chart 1) will assist in establishing a random ordering at every step of the 
experiment. 



Statistical tests 



In general, discriminative tests are analyzed by comparing test statistics 
with chart values; ranking test results are analyzed by calculation of a 
Friedman statistic; structured, unstructured, and ratio scale tests with two 
samples are analyzed by a t-test; and tests with more than two samples are 
analyzed by an F-test. The following analyses are described in the text: 

• triangle test (page 20) 

• duo-trio test (page 22) 

• two-out-of-five test (page 23) 

• paired comparison test (page 25) 

• Friedman for ranked data (page 26) 

• £-test (page 32) 

• analysis of variance (page 36) 

• analysis of variance with interactions (page 42) 

• analysis of variance of logarithmically transformed data (page 48). 

When there are more than two treatments, the sensory analyst may 
wish to know more than whether there is a significant difference among the 
samples. Use of a multiple comparison test can determine which pairs of 
means are significantly different. Multiple comparison tests are not always 
appropriate. Available multiple comparison tests include Scheffe, Tukey, 
Newman-Keuls, Duncan's multiple range, and Fisher's LSD. A more 
powerful test (e.g., Fisher's LSD) has a smaller least significant difference 



18 



(LSD) and therefore a greater likelihood of finding a difference. However, 
there is also the risk of finding such a difference regardless of whether or 
not one exists. On the other hand, a more conservative test (e.g., Tukey's) 
has a larger LSD and therefore is less likely to find a difference between the 
means. A Dunnett test is a multiple comparison test designed for a special 
application; it is used only when all the means are compared to one of the 
means, for example, a control. In some cases, such as increasing or 
decreasing concentrations of a factor, it is more appropriate to perform a 
linear regression on the samples. This will determine the degree of 
association between two sets of data, namely, sensory results and the factor 
under study. The reader can find details of each of these tests in Sensory 
evaluation of food — Statistical methods and procedures (O'Mahony 1986). 
The following comparison tests are described in the text: 

• multiple comparison test (Tukey's) for scaling (page 38) 

• multiple comparison test for ranks (page 28) 

• comparison of control (Dunnett's) to other scores (page 45) 

• estimation of linear regression (page 49). 



Sensory analysis test methods 



Several different sensory analysis methods are now available. The 
researcher should be thoroughly familiar with the advantages and 
disadvantages of each method. Choose the most practical and efficient 
method for each situation. No one method can be used universally. The 
researcher must precisely define the purpose of the test and the 
information sought from it. 

The three fundamental types of sensory tests are discriminative tests, 
descriptive tests, and affective tests. We use discriminative tests to 
determine whether a difference exists between samples. We use descriptive 
tests to determine the nature and intensity of the differences. Affective 
tests are based on either a measure of preference (or acceptance) or a 
measure from which we can determine relative preference. The personal 
feelings of panelists toward the product directs their response. In this 
publication, we describe several commonly used experimental methods 
with examples of the questionnaires, their application, and statistical 
analysis. 



Discriminative tests 



Sensory analysis is often conducted to determine whether or not a 
difference exists among samples. Testing for "sameness" is referred to as 
"similarity" testing. Typically in quality control this type of testing 
predominates. It is necessary then to minimize p (Type II error). Testing to 
find a difference is referred to as "discriminative" (difference) testing. The 



19 



ot value (Type I error) is therefore minimized. We direct the reader to 
Meilgaard et al. (1987 a,b) for a more detailed explanation of similarity and 
difference testing. The latter is a common situation in quality maintenance, 
cost reduction, selection of new sources of supply, and storage stability 
studies. Several different sensory methods allow us to determine 
differences. The difference tests included in this publication are triangle 
test, duo-trio test, two-out-of-five test, paired comparison test, and 
ranking test. We discuss the advantages, disadvantages, and special 
features of each test. 



Triangle test 

The results of a triangle test indicate whether or not a detectable difference 
exists between two samples. Higher levels of significance do not indicate 
that the difference is greater but that there is a greater probability of a real 
difference. 

The panelist receives three coded samples, is told that two of the 
samples are the same and one is different, and is asked to identify the odd 
sample. This method is useful in quality control work to determine if 
samples from different production lots are different. It is also used to 
determine if ingredient substitution or some other change in 
manufacturing results in a detectable difference in the product. The 
triangle test is often used in selecting panelists. 

Because the panelist is looking for the odd sample, the samples should 
differ only in the variable being studied. Mask all other differences. 
Therefore, application of the triangle test is limited to products that are 
homogeneous. 

Analysis of the results of triangle tests is based on comparing the 
number of correct identifications actually received with the number you 
would expect to get by chance alone if there were no difference between the 
samples. In the triangle test we would expect the odd sample to be selected 
by chance one-third of the time. 

To determine the probability that the different sample was correctly 
identified by chance alone (no detectable difference), use Statistical 
Chart 2 (Appendix). 

With the triangle test, neither are the size and direction of the 
difference between samples determined nor is there any indication of the 
characteristic responsible for the difference. 

There are six possible ways in which the samples in a triangle test can 
be presented: 

ABB BBA AAB 
BAB ABA BAA 



Indicate the order in which each panelist should taste the samples by 
putting the code numbers in the appropriate order on the score sheet. 



20 



In most cases, each sample is used as the duplicate for half the tests and 
as the different sample for the other half. In some cases it has been found 
that more correct identifications are received when the duplicate samples 
are the normal or control samples. A sample of the questionnaire and an 
example of the triangle test follow. 




QUESTIONNAIRE FOR TRIANGLE TEST 

PRODUCT: Canned tomatoes 

NAME DATE 



Two of these three samples are identical, the third is different. Taste the 
samples in the order indicated and identify the odd or different sample. 

Identify the odd or different sample. 

Code Check odd or different sample 

314 

628 

542 



Comments: 



Example A triangle test was used to determine if there was a detectable 
difference between canned tomatoes processed under two different sets of 
conditions. 

Samples were served in coded dishes to 36 panelists. Each panelist 
received three coded samples: 18 panelists tested two samples from 
treatment A and one from treatment B; the other 18 panelists received one 
sample from treatment A and two from treatment B. Because of the nature 
of the presentation, it was necessary to assign two code numbers to each 
treatment. The results are shown in Table 1. 



Treatment Code Number of samples required 



A 314 18 

542 36 

B 628 36 

149 18 



21 



Table 1 Triangle test on canned tomatoes processed by treatment A or 
treatment B 







Odd sample chosen 




Code (treatment) 


Correct 


Incorrect 


Total 


314(A) 628(B) 542(A) 
542(A) 628(B) 149(B) 

Total 


9 
12 

21 


9 
6 

15 


18 
18 

36 



The odd sample was correctly identified by 21 panelists. According to 
the Statistical Chart 2 (Appendix), 21 correct judgments out of 36 in a 
triangle test indicate a probability of 0.002, which is less than the critical 
value of P = 0.05. Thus the probability of getting these results by chance is 
2 in 1000. We conclude that a detectable difference existed between the 
samples. 

Duo-trio test 

In the duo-trio test, three samples are presented to the panelist; one is 
labeled R (reference) and the other two are coded. One coded sample is 
identical with R and the other is different. The panelist is asked to identify 
the odd sample. This test is similar to the triangle test, except that, one of 
the duplicate samples is identified as the reference (R). 

The duo-trio test has the same applications as the triangle test but is 
less efficient because the probability of selecting the correct sample by 
chance is 50%. Often panelists find this test easier than the triangle test. 
This test is often used instead of the triangle test when evaluating samples 
that have a strong flavor because fewer comparisons are required. The two 
coded samples do not have to be compared to each other. 

For the duo-trio test either one of the samples can be selected for use as 
the reference throughout the whole test or the two samples can be used 
alternately as the reference. The quantity of the R sample should be about 
double that of the coded samples. 

Determine the likelihood that the number of correct identifications 
was obtained by chance alone (no detectable difference). The duo-trio is 
always a one-tailed test (see "Paired comparison test"). Use Statistical 
Chart 4 (Appendix) to determine this probability. A sample of the 
questionnaire and an example of the duo-trio test follow. 



22 






QUESTIONNAIRE FOR DUO-TRIO TEST 

PRODUCT: Cheddar cheese 

NAME DATE 



On your tray you have a marked control sample (R) and two coded samples. 
One sample is identical with R and the other is different. 

Which of the coded samples differs from R? 

Code Check odd or different sample 

432 

701 



Comments: 



Example A duo-trio test was used to determine if methional could be 
detected when added to cheddar cheese at 0.250 ppm. The duo-trio test was 
used in preference to the triangle test because less tasting- is required to 
form a judgment. This fact is important when panelists taste a substance 
with a lingering aftertaste, such as methional. 

The test was performed using 16 panelists. The panelists were 
presented with a tray on which were a coded sample containing 0.250 ppm 
methional and two control samples, one R and one coded. The order of 
presentation of the two coded samples was randomized. A total of 16 
judgments were made. The results showed that, of the 16 judgments made, 
14 correct identifications were obtained. 

Consult Statistical Chart 4 (Appendix) for 16 panelists in a two-sample 
test. This chart shows that 14 correct judgments has a probability of 0.002, 
which is less than the critical value of P = 0.05. We conclude that 
methional added to cheddar cheese was detectable at the 0.250 ppm level. 

As with the triangle test, the duo-trio test can establish if a detectable 
difference exists between samples. However, it does not indicate the size of 
the difference or whether the panelists' identifications of the odd sample 
were based on the same characteristic. 

Two-out -of -five test 

The panelist receives five coded samples, is told that two of the samples 
belong in one set and three to another, and is asked to identify the two 
samples that belong together. 

This method has applications similar to the triangle test. It is 
statistically more efficient than the triangle test because the probability of 



23 



guessing the right answer in the two-out-of-five test is 1 in 10, compared to 
1 in 3 for the triangle test. However, this test is strongly affected by sensory 
fatigue. It is recommended for visual, auditory, and tactile testing rather 
than flavor and odor. 

Analysis of the results of the two-out-of-five test is based on the 
probability that if there were no detectable difference, the correct answer 
would be given one-tenth of the time. A table for rapid analysis of 
two-out-of-five data is presented in Statistical Chart 5 (Appendix). 

The results of the two-out-of-five test indicate if there is a detectable 
difference between two sets of samples. No specific characteristic can be 
identified as responsible for the difference. 

Twenty presentation orders are possible in the two-out-of-five test: 



AAABB 


ABABA 


BBBAA 


BABAB 


AABAB 


BAABA 


BBABA 


ABBAB 


ABAAB 


ABBAA 


BABBA 


BAABB 


BAAAB 


BABAA 


ABBBA 


ABABB 


AABBA 


BBAAA 


BBAAB 


AABBB 



If 20 panelists are not used, select at random from the possible 
combinations using three As for half and three Bs for half. A sample of the 
questionnaire and an example of the two-out-of-five test follow 



QUESTIONNAIRE FOR TWO-OUT-OF-FIVE TEST 



PRODUCT: Wieners 

NAME 



DATE 



Two of these five samples belong to one set; the other three belong to 
another set. Examine the color of the samples in the order listed below 

Identify the two samples which belong together by placing an x after the 
code numbers. 

Code 

846 

165 

591 

497 

784 

Comments: 



24 



Example A two-out-of-five test was used to determine if a different curing 
agent changed the color of wieners. Coded samples were presented to 20 
panelists who were asked to examine them visually. The method of 
evaluation specified depends on the purpose of the test, e.g., listen to the 
crunch when chewed, or feel the roughness of the sample. 
The number of correct responses was counted: 

Total responses: 20 

Correct responses: 7 

According to Statistical Chart 5 (Appendix), 7 correct responses from 
20 panelists indicates a difference significant at P = 0.002. We conclude 
that a significant difference in color existed between the samples. 

Paired comparison test 

In this test, the panelist receives a pair of coded samples and is asked to 
compare for the intensity of some particular characteristic. The panelist is 
asked to indicate which sample has greater intensity of the characteristic 
being studied. 

The paired comparison test is used to determine if two samples differ in 
a particular characteristic. The difference tests, except two-out-of-five, 
presented up to now did not specify any particular characteristic; panelists 
based their answers on any detectable difference. The paired comparison 
test can be used for quality control, to determine if a change in production 
has resulted in a detectable difference. It can also be used in selecting 
panelists. The probability of a panelist selecting a sample by chance is 50% 
in the paired comparison test. 

In a paired comparison test, one sample is usually expected to have 
greater intensity of the characteristic being evaluated. This is a directional 
difference test, so we use a one-tailed test (Statistical Chart 4 in 
Appendixes). However, when there is no expectation about the result, use a 
two-tailed test (Statistical Chart 3 in Appendixes). 

Paired comparison tests give no indication of the size of the difference 
between the two samples but determine whether there is a detectable 
difference in a particular characteristic and the direction of the difference. 
A sample questionnaire and example for a paired comparison test follow. 



25 



QUESTIONNAIRE FOR PAIRED COMPARISON TEST 

PRODUCT: Canned peaches 

NAME DATE 



Evaluate the sweetness of these two samples of canned peaches. Taste the 
sample on the left first. 

Indicate which sample is sweeter by circling the number. 

581 716 

Comments: 

Example To determine if there was a difference in sweetness between 
peaches canned in liquid sucrose at 45 ° Brix or in a 52% invert syrup at 45 ° 
Brix, a paired comparison test was used. 

Peaches from each treatment were served in coded dishes to 20 
panelists. Ten panelists were asked to taste one sample first; 10 were asked 
to taste it second. Twelve panelists chose the 52% invert syrup sample as 
sweeter. Invert syrup is generally considered to be sweeter than sucrose at 
the same concentrations; thus a one-tailed test is used. According to 
Statistical Chart 4 (Appendix), in a paired comparison test the probability 
is 0.252, which is greater than the critical value of P = 0.05. Therefore, we 
conclude that no detectable difference existed in sweetness between the 
two treatments. 

Ranking test (Friedman) 

The ranking test is an extension of the paired comparison test. The panelist 
receives three or more coded samples and is asked to rank them for the 
intensity of some specific characteristic. 

The ranking method is rapid and allows several samples to be tested at 
once. It is generally used to screen one or two samples from a group rather 
than to test all samples thoroughly. The results of a ranking test can be 
checked for significance using the Friedman test for ranked data. No 
indication of the size of the differences between samples is obtained. 
Samples ranked one after the other may differ greatly or only slightly but 
they are still separated by a single rank unit. Because samples are evaluated 
only in relation to each other, results from one set of ranks cannot be 
compared with the results from another set of ranks unless both contain 
the same samples. If ties are permitted, an alternative test statistic must be 



26 



used, the reader is directed to Meilgaard et al. (1987a). A sample 
questionnaire and an example of the ranking" test follow. 



QUESTIONNAIRE FOR RANKING TEST 

PRODUCT: Fruit drink 

NAME DATE 



Rank these samples for sweetness. The sweetest sample is ranked first, the 
second sweetest sample is ranked second, the third sweetest sample is 
ranked third, and the least sweet sample is ranked fourth. Test the samples 
in the order indicated. 

Place the code numbers on the appropriate lines. 

212 336 471 649 

Ranking: Most sweet 1. 

2. 

3. 

Least sweet 4. 

Comments: 



Example A ranking test was used to compare the sweetness of a fruit 
drink made using four different sweetening agents. Eight panelists ranked 
the four drinks using the score sheet above. The ranks given the samples by 
the panelists are shown in Table 2. 



27 



Table 2 Rank scores of four sweetening agents in fruit drink 







Treatments 






Panelists 


A 


B 


C 


D 




(212) 


(336) 


(471) 


(649) 


1 


4 


2 


1 


3 


2 


4 


3 


1 


2 


3 


3 


1 


2 


4 


4 


3 


2 


1 


4 


5 


4 


1 


2 


3 


6 


4 


3 


1 


2 


7 


4 


2 


1 


3 


8 


4 


1 


2 


3 


Rank sum 


30 


15 


11 


24 



Friedman test 
ranked data: 



The results are analyzed using the Friedman test for 



First calculate test statistic, T. 

T = {12/[number of panelists x number of treatments x (number of 
treatments + 1)]} x (sum of the squares of the rank sum of each 
treatment) - 3 (number of panelistsHnumber of treatments + 1) 

= [12/(8 X 4 x 5)] X (30 2 + 15 2 + ll 2 + 24 2 ) - 3(8 X 5) 

= (12/160) X 1822 - 120 

= 136.65 - 120 

= 16.65. 

When the number of judgments are sufficiently large, use Statistical 
Chart 6 (Appendix) to find the value of chi-square, x 2 > with 3 degrees of 
freedom for a = 0.05. The appropriate degrees of freedom are determined 
as one less than the number of samples. The value is 7.81. Exact 
probabilities are available in O'Mahony (1986) for small numbers of 
treatments and panelists. 

The calculated value of T is 16.65. This is greater than the critical value 
of 7.81, so we conclude that a significant difference in sweetness existed 
among the samples (P < 0.05). 

Treatments that are significantly different from one another can be 
determined using a test given in Hollander and Wolfe (1973) and illustrated 
here. This is used when a multiple-range test is appropriate (see Statistical 
tests). For less than eight panelists, exact values are given in Newell and 
MacFarlane (1987). 

The least significant difference is determined using Statistical Chart 7 
(Appendix). In this case, there were four treatments. The values listed 
under infinite degrees of freedom for error are always used for this rank 



28 



test. The value is 3.63. The least significant difference is calculated as 
follows: 

LSD rank = 3.63 /[No. panelists x No. treatments x (No. treatments + l)]/l2 



> 


13.3 


< 


13.3 


< 


13.3 


> 


13.3 


< 


13.3 



= 3.63 7(8 x 4 x 5)/12 

= 3.63 713.33 

= 13.3. 

Any two samples where rank sums differ by more than 13.3 are 
significantly different. 

Compare C with each of the other samples: 

A - C = 30 - 11 = 19 

D - C = 24 - 11 = 13 

B - C = 15 - 11 = 4 
therefore C is significantly sweeter than A. 

Compare B with the others: 

A - B = 30 - 15 = 15 

D - B = 24 - 15 = 9 
therefore B is significantly sweeter than A. 

Then compare D and A: 

A-D = 30-24= 6< 13.3 
These results can be shown by using letters to indicate differences: 

C B D A 

Rank sum 11a 15a 24ab 30b 

Average rank 1.4 1.9 3 3.8 

Any two rank sums not followed by the same letter are significantly 
different (P < 0.05). C and B are significantly sweeter than A. 

A test for all treatments versus control is also available (Newell and 
MacFarlane 1987) and should be used when appropriate. 



Descriptive tests 



The sensory analyst is often interested in obtaining more information than 
just "Is there a difference?" Descriptive analysis can be used to identify 
sensory characteristics that are important in a product and give 
information on the degree or intensity of those characteristics. This 
provides an actual sensory description of test products. Descriptive 
information can help in identifying ingredient or process variables 
responsible for specific sensory characteristics of a product. This 
information can be used to develop new products, to improve products or 
processes, and to provide quality control. This section is divided into two 
parts. The first part describes three different scales that can be used to 
measure the perceived quantity of specified sensory characteristics. The 



29 



second part presents three descriptive analysis methods used to obtain a 
descriptive profile of a product and an example of a panel procedure used at 
the Food Research Centre. 



Scaling methods 

Structured scaling 

Structured or category scales provide panelists with an actual scale 
showing several degrees of intensity or magnitude of a perceived sensory 
characteristic. The intensities or response categories of the sensory 
attribute can be labeled with numbers, words, or a combination of the two. 
Usually the number of response categories used ranges from 6 to 10. A 
number or words (or both) can be assigned to each response category, just 
to the extremes, or to any combination of the two. Panelists can evaluate 
one to several sensory characteristics at a time for one or more products. 

Descriptive words on the scale must be carefully selected and the 
panelists trained so that they agree on the meaning of the terms. Objective 
terms, such as "very hard," rather than preference terms, such as "much 
too hard," must be used. Panelists are not typical consumers and their likes 
and dislikes are not solicited. The scale must also be labeled, indicating an 
increase or decrease in the intensity of the characteristic being measured. 
A scale running from extremely sweet to extremely sour is incorrect, 
because sweet and sour are not opposites. A product can be both sweet and 
sour at the same time. Two scales must be used, one for sweetness (no 
sweetness to extremely sweet) and one for sourness (no sourness to 
extremely sour). Opposites are used with a bipolar scale (e.g., hard to soft). 

Certain problems are inherent with structured scales, of which the 
researcher should be aware. The psychological distance or sensory interval 
between two descriptors might not always be equal. For example, a scale 
used to measure perceived sweetness of a beverage might include the terms 
"extremely sweet, very sweet, moderately sweet, slightly sweet, trace of 
sweetness, not sweet." The psychological distance between "extremely 
sweet" and "very sweet" is not necessarily the same as between "trace of 
sweetness" and "not sweet." However, the numerical distance in each case 
is one. Also, panelists usually avoid the extreme points on the scale, 
believing that another sample might have an even higher or lower intensity 
of the sensory characteristic (central tendency error). A nine-point scale, 
for example, is used as if it were a seven-point scale. To use structured 
scales effectively, all the panelists must be judging the same characteristic; 
their use is not a problem when a simple characteristic like sweetness is 
involved. When a complex characteristic is judged (for example, the 
"texture" of cheese) it must be characterized into individual components, 
such as hardness, cohesiveness, fat properties, and so on, and each one 
evaluated. All panelists may not have the same concept and therefore need 
training. 

Including standards at various points on the scale helps to minimize 
panel variability. These standards act as anchors in counteracting the 



30 



tendency of scales to drift in meaning with time. This instability is a 
marked disadvantage when structured scales are used in storage stability 
studies over an extended time. A sample of the questionnaire and an 
example of a structured scale follow. 



QUESTIONNAIRE FOR STRUCTURED SCALE 



PRODUCT: Cheddar cheese 

NAME 



DATE 



Evaluate these cheese samples for bitterness. 

Indicate the amount of bitterness in each sample on the scales below. 



590 

- not bitter 

- slightly bitter 

- moderately bitter 

- very bitter 

- extremely bitter 



172 

- not bitter 

- slightly bitter 

- moderately bitter 

- very bitter 

- extremely bitter 



Comments: 



Example The structured scale was used to determine 
bitterness in cheddar cheese made using two different 
enzymes. Samples of cheese from each treatment 
presented to 20 panelists for evaluation. The order of 
balanced so that each order (AB, BA) was used 10 times, 
were assigned to the scale with "not bitter" equal to 1 
bitter" equal to 9. The scores are tabulated (Table 3). 



any difference in 
milk-coagulating 
were coded and 
presentation was 
Numerical scores 
up to "extremely 



31 



Table 3 
samples 



Scores using a structured scale to measure bitterness in cheese 



Panelist 



Treatments 






A 


B 


Difference 


(590) 


(172) 


(A-B) 


4 


4 





5 


4 


1 


5 


2 


3 


5 


2 


3 


2 


4 


-2 


5 


4 


1 


6 


3 


3 


6 


3 


3 


7 


3 


4 


4 


1 


3 


6 


2 


4 


3 


2 


1 


6 


4 


2 


5 


5 





2 


3 


-1 


3 


3 





6 


2 


4 


4 


1 


3 


4 


4 





5 


5 





93 


61 


32 


4.7 


3.1 


1.6 



1 

2 

3 

4 

5 

6 

7 

8 

9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

Total 
Mean 



In this example, each panelist compared two samples. A paired £-test is 
used to analyze the data. This test assumes that the intervals between 
categories are equal, which may not be the case. Therefore the results 
should be considered approximate. Alternatively the data could be 
examined using a paired comparison test or a Wilcoxin signed rank test as 
described by O'Mahony (1986). 

Analysis using t-test 

Calculate d (average difference): 

d = mean for A - mean for B 
= 4.7-3.1 
= 1.6 



32 



Calculate S: 



S = J{Zd 2 - [(2d) 2 /n]}/(n-l) 

where: Xd 2 = sum of the square of each difference 

= 2 + l 2 + 3 2 + ... + 2 = 114 

(Xd) 2 = sum of the differences, squared 

= 32 2 = 1024 

n = number of pairs = 20 

therefore: S = /(114 - 1024/20)/19 = 1.82 

Find the t value from Statistical Chart 8 (Appendix) under the column 
headed 0.05. 

The df is the number of pairs minus one: 

df = 20 - 1 = 19 

rvalue = 2.093 

d 
The samples are significantly different if — > t 

d = L6 = 3 93 

S/JK 1.82/720 

In this example 3.93 is greater than the t value, 2.093. 

Using a paired comparison test as an alternative, we note there are 13 
positive differences out of 15 nonzero differences. From Statistical Chart 3 
the probability of this event under the null hypothesis is 0.007. Thus both 
test methods agree there is a difference in the two samples. 

We conclude that cheese A was significantly more bitter than cheese B 
(P < 0.05). 



Unstructured scaling 

An alternative to the structured scale is an unstructured scale, also called 
line or visual analogue scales. In sensory analysis the unstructured scale 
most often used consists of a horizontal line 15 cm long with anchor points 
1.5 cm from each end and often, but not necessarily, a mid point. Each 
anchor point is usually labeled with a word or expression. A separate line is 
used for each sensory attribute to be evaluated. Panelists record each 
evaluation by making a vertical line across the horizontal line at the point 
that best reflects their perception of the magnitude of that property 
(Fig. 5). 

After the panelists have completed their judgments, the researcher 
measures the distance from the left end point of the line to each point 
marked by the panelist. The researcher then records the distances as 
intensity ratings between 0.0 and 15.0 for each product evaluated and 
analyzes these ratings. 



33 



Unstructured scales eliminate the problem of unequal intervals that is 
associated with structured scales. The terms to be used at the anchor points 
of the lines are agreed upon during* panel training. These scales also 
represent a continuum and the comments under structured scaling apply. 

A sample questionnaire and an example of descriptive analysis with an 
unstructured scale follow. 



QUESTIONNAIRE FOR UNSTRUCTURED SCALING 



PRODUCT: Wieners 

NAME 



DATE 



Please evaluate the hardness and chewiness of these sample of wieners. 
Make a vertical line on the horizontal line to indicate your rating of the 
hardness and chewiness of each sample. Label each vertical line with the 
code number of the sample it represents. 



Please taste the samples in the following order: 
572 681 437 



249 



1. Hardness- 



■the force required to compress the wiener sample 
between the molar teeth 



very soft 
2. Chewiness- 



very hard 

-the perceived work required to reduce the wiener 
sample to a consistency ready for swallowing 



slightly chewy 
Comments: 



very chewy 



Example This method was used when studying the texture of wieners. 
During preliminary testing the panelists determined that hardness and 
chewiness were the most important textural characteristics of wieners. 
The anchor words and definitions were agreed upon by the panel during 
preliminary sessions. Four brands of wieners were evaluated by eight 
panelists using the questionnaire. 



34 




Fig. 5 Tray prepared for an unstructured scaling test. 



Numerical values were given to the ratings by measuring the distance 
of the panelists' marks from the left end of the line in units of 0.1 cm 
(Table 4). Analysis of variance was conducted on the numerical values for 
each characteristic. 



Table 4 Hardness scores of four brands of wieners 









Treatments (Code) 






Panelist 


A 


B 


C 


D 


Total 




(249) 


(681) 


(437) 


(572) 




1 


4.8 


5.3 


8.5 


2.8 


21.4 


2 


10.3 


6.0 


12.8 


7.5 


36.6 


3 


11.5 


8.0 


13.3 


4.5 


37.3 


4 


5.8 


13.3 


13.3 


3.3 


35.7 


5 


3.8 


11.8 


13.3 


1.5 


30.4 


6 


5.0 


8.3 


11.8 


4.5 


29.6 


7 


5.0 


8.8 


13.0 


6.8 


33.6 


8 


5.3 


12.0 


13.5 


4.3 


35.1 


Total 


51.5 


73.5 


99.5 


35.2 


259.7 


Mean 


6.44 


9.19 


12.44 


4.40 





35 



Analysis of variance 

To complete an analysis of variance, certain calculations must be 
performed to determine the correction factor (CF), the sum of squares 
(SS), the degrees of freedom (df), the mean square (MS), and the variance 
ratio (or F value). A detailed explanation of these calculations using the 
results from Table 4 follows. This analysis can also be performed using a 
statistical package. 

Correction factor The correction factor (CF) is calculated by squaring the 
total and dividing by the total number of judgments. 

CF = 259.7 2 /(8 x 4) 
= 67 444.09/32 
= 2107.63 

Sum of squares (treatments) The sum of squares for treatments (S S(Tr)) 
is calculated by adding the squares of the total for each treatment, dividing 
by the number of judgments for each treatment, and then subtracting the 
correction factor. 

SS(Tr) = [(51.5 2 + 73.5 2 + 99.5 2 + 35.2 2 )/8] - CF 
= [19 193.79/8] - CF 
= 2399.22-2107.63 
= 291.59 

Sum of squares (panelists) The sum of squares for panelists (SS(P)) is 
calculated by adding the squares of the total for each panelist, dividing by 
the number of judgments made by each panelist, and subtracting the 
correction factor. 

SS(P) = [(21.4 2 4- 36.6 2 + 37.3 2 + 35.7 2 + 30.4 2 + 29.6 2 + 33.6 2 + 35.1 2 )/4] - CF 

= 8624.59/4 -CF 

= 2156.15-2107.63 

= 48.52 

Sum of squares (total) The sum of squares for the total (SS(T)) is 
calculated by adding the square of each judgment and subtracting the 
correction factor. 

SS(T) = (4.8 2 + 10.3 2 + 11.5 2 + 5.8 2 + 3.8 2 + 5.0 2 + 5.0 2 + 
5.3 2 + 5.3 2 + 6.0 2 + 8.0 2 + 13.3 2 + 11.8 2 + 8.3 2 + 
8.8 2 + 12.0 2 + 8.5 2 + 12.8 2 + 13.3 2 + 13.3 2 + 13.3 2 + 
11.8 2 + 13.0 2 + 13.5 2 + 2.8 2 + 7.5 2 + 4.5 2 + 3.3 2 + 
1.5 2 + 4.5 2 + 6.8 2 + 4.3 2 ) - CF 
= 2561.81-2107.63 
= 454.18 
Sum of squares (error) The sum of squares for error (SS(E)) is calculated 
by subtracting the SS values obtained from all specified sources of 
variation (treatments, panelists) from the SS for the total. 



36 



SS(E) = 454.18-291.59-48.52 
= 114.07 

Degrees of freedom (treatments) The degrees of freedom for treatments 
(df(Tr)) are calculated by subtracting one from the number of treatments. 

df(Tr) =4-1 
= 3 

Degrees of freedom (panelists) The degrees of freedom for panelists 
(df(P)) are calculated by subtracting one from the number of panelists. 

df(P) = 8-1 

= 7 

Degrees of freedom (total) The degrees of freedom for total (df(T)) are 
calculated by subtracting one from the total number of judgments. 

df(T) =32-1 
= 31 

Degrees of freedom (error) The degrees of freedom for error (df(E)) are 
determined by subtracting the df for the other sources from the df for the 
total. 

df(E) = 31-7-3 
= 21 

Mean square The mean square (MS) for any variable is determined by 
dividing the sum of squares (SS) for that variable by its respective degrees 
of freedom (df). 

MS(Tr) = 291.59/3 

= 97.20 

MS(P) = 48.52/7 

= 6.93 

MS(E) = 114.07/21 

= 5.43 

Variance ratio (treatments) The variance ratio or F value for treatments 
(F(Tr)) is determined by dividing the MS for treatments by the MS for 
error. 

F(Tr) = 97.20/5.43 
= 17.9 

Variance ratio (panelists) The F value for panelists (F(P)) is determined 
by dividing the MS for panelists by the MS for error. 

F(P) = 6.93/5.43 
= 1.3 

The analysis of variance is summarized in Table 5. 



37 



Table 5 Analysis of variance of hardness of wieners 



Source of variation 


df 


SS 


MS 


F 


Treatments 
Panelists 
Error 
Total 


3 

7 

21 

31 


291.59 

48.52 

114.07 

454.18 


97.20 
6.93 
5.43 


17.9** 
1.3 


**P < 0.01. 











To determine if the difference among the treatments is significant, the 
calculated F value (17.9) is checked on Statistical Chart 9 (Appendix). With 
three degrees of freedom in the numerator and 21 degrees of freedom in the 
denominator, the variance ratio (F value) must exceed 3.07 to be significant 
at a probability of 0.05 (*) and must exceed 4.87 to be significant at 
P < 0.01 (•*). The value 17.9 is therefore significant at the 0.01 probability 
level. We therefore conclude that there was a difference in hardness among 
the four brands of wieners. 

Tukey's test 

The treatments that are different from each other can be determined using 
Tukey's multiple comparison test (Snedecor and Cochran 1989). Multiple 
comparison tests (e.g., Scheffe, Tukey's, Newman-Keuls, Duncan's, and 
Fisher's LSD) are useful yardsticks for comparing means from qualitative 
treatments with no obvious order, such as those four brands of wieners. But 
multiple comparisons are not appropriate when 

• treatments are levels of a quantitative variable, such as sugar added to 
coffee at 5, 10, or 15%; 

• treatments are factorial combinations of factors, that is, each level of 
every factor occurs with each level of every other; 

• comparisons of particular interest are noted at the planning stage. 

For discussion of the alternatives to multiple comparison tests see 
Petersen (1977) or Little (1978). 

The standard error of the treatment mean is calculated here using 

Table 5. 

Standard error of the treatment mean The standard error of the 
treatment mean (SEM) is calculated by taking the square root of the MS for 
error divided by the number of judgments for each sample. 

SEM = /5.43/8 

- /068 
= 0.82 



38 



The significant studentized range value at P = 0.05 from Statistical 
Chart 7 (Appendix) for four treatments and 20 degrees of freedom is 3.96. 
For 21 degrees of freedom the interpolated value would be about 3.95. 

Least significant difference The least significant difference (LSD) is 
calculated by multiplying the value obtained from the table by the SEM. 

LSD = 3.95 X 0.82 
= 3.24 

Any two treatment means that differ by 3.24 or more are significantly 
different at P < 0.05. 

Arrange the treatment according to magnitude. 

C B A D 

12.44 9.19 6.44 4.40 

Compare each mean with the others to see if the difference is 3.24 or more. 

C - D = 12.44 - 4.40 = 8.04 > 3.24 
C - A = 12.44 - 6.44 = 6.00 > 3.24 
C - B = 12.44 - 9.19 = 3.25 > 3.24 

therefore C differs significantly from all the others. 

B - D = 9.19 - 4.40 = 4.79 > 3.24 
B - A = 9.19 - 6.44 = 2.75 < 3.24 

therefore B differs significantly from D but not from A. 

A - D = 6.44 - 4.40 = 2.04 < 3.24 

therefore A and D are not significantly different. 

The results are shown using letters to indicate differences. Although 
additional decimal places are carried throughout to maintain accuracy, the 
results are presented to one decimal place. Any two values not followed by 
the same letter are significantly different at P < 0.05. 

C B A D 

12.4a 9.2b 6.4bc 4.4c 

Unstructured scaling with replication 

The second example of unstructured scaling that follows is one of an 
analysis of variance with replication using a control. This example would be 
typical of data from a trained panel. Consumer evaluations are not 
replicated. 

Example The juiciness of apples was evaluated. Each panelist received 
four apples, one for each of four different varieties (treatments) on each of 
three days (replicates). X was the control. The three new varieties were A, 
B, and C. The effects of treatments, panelists, replications, and their 
interactions were partitioned out (Table 6). For details of the method of 
analysis of variance see the previous example. 



39 



Table 6 Juiciness scores for apples 















Treatments 
















X 






A 






B 






C 






Panelist 


Replication 


Replication 


Replication 


Replication 


Total 




1 


2 


3 


1 


2 


3 


1 


2 


3 


1 


2 


3 




1 


8.5 


7.1 


5.6 


7.9 


8.2 


7.9 


10.4 


9.4 


7.7 


6.1 


6.2 


6.3 


91.3 


2 


7.2 


7.0 


6.8 


7.8 


7.0 


8.2 


9.9 


9.2 


8.9 


8.1 


7.4 


7.8 


95.3 


3 


8.4 


6.1 


6.6 


7.6 


7.8 


5.9 


9.7 


8.4 


7.4 


6.7 


6.4 


6.3 


87.3 


4 


7.3 


4.5 


7.8 


7.9 


7.2 


6.7 


9.0 


8.6 


9.5 


7.4 


5.5 


4.7 


86.1 


5 


6.4 


7.1 


4.4 


6.9 


6.8 


6.0 


6.7 


9.0 


7.6 


5.8 


3.4 


5.0 


75.1 


6 


8.0 


6.3 


7.7 


7.5 


7.0 


7.1 


8.6 


9.2 


9.7 


7.0 


6.7 


6.4 


91.2 


7 


6.9 


5.4 


6.1 


7.4 


7.2 


7.1 


8.5 


7.5 


7.8 


5.0 


4.4 


4.8 


78.1 


8 


8.2 


6.0 


5.8 


7.3 


6.0 


7.3 


7.9 


8.6 


8.7 


5.3 


4.0 


5.0 


80.1 


Treatment by replication total 
60.9 49.5 50.8 60.3 


57.2 


56.2 


70.7 


69.9 


67.3 


51.4 


44.0 


46.3 


684.5 


Treatment tota] 






























X = 


161.2 




A = 


173.7 




B = 


207.9 




C = 


141.7 




Replication total 






1 = 


243.3 




2 = 


220.6 




3 = 


220.6 





Correction factor: 

» 

CF = Total 2 /number of responses 
= (684.5 2 )/(8 X 4 x 3) 
= 4880.63 

Sum of squares (treatments): 

SS(Tr) = (Sum of squares of the total for each treatment/number 
of judgments for each treatment) - CF 
= [Q61.2 2 + 173.7 2 + 207.9 2 + 141.7 2 )/24] - CF 
= 4977.44-4880.63 
= 96.81 
Sum of squares (panelists): 

SS(P) = (Sum of squares of the total for each panelist/number 
of judgments for each panelist) - CF 
= [(91.3 2 + 95.3 2 + 87.3 2 + ... + 80.1 2 )/12] - CF 
= 4910.45-4880.63 
= 29.82 



40 



Sum of squares (replicates): 

SS(R) = (Sum of squares of the total for each replicate/number 
of judgments in each replicate) - CF 
= [(243.3 2 + 220.6 2 + 220.6 2 )/32] - CF 
= 4891.36-4880.63 
= 10.73 
Sum of squares (total): 

SS(T) = (Sum of squares of the total for each judgment) - CF 
= (8.5 2 + 7.2 2 + 8.4 2 + ... + 4.8 2 + 5.0 2 ) - 4880.63 
= 5068.93-4880.63 
= 188.30 

Sum of squares (error): 

SS(E) = SS(T) - SS(Tr) - SS(P) - SS(R) 
= 188.30 - 96.81 - 29.82 - 10.73 
= 50.94 

The analysis of variance is summarized in Table 7. 
Table 7 Analysis of variance of apple juiciness 



Source of variation 


df 


SS 


MS 


F 


Replicates 
Panelists 
Treatments 
Error 


2 

7 

3 

83 


10.73 
29.82 
96.81 
50.94 


5.37 

4.26 

32.27 

0.61 


8.8** 

7.0** 

52.9** 


**P < 0.01. 











With three degrees of freedom in the numerator and 83 degrees of 
freedom in the denominator, the variance ratio (F value) must exceed an 
estimated 2.7 to be significant at P < 0.05 (*) and about 4.0 to be significant 
atP < 0.01 (**) (Statistical Chart 9 in Appendixes). The calculated F value 
is 52.9 for treatments. There is a significant difference at P < 0.01 (**). 

There is also a significant panelist effect and a significant replicate 
effect at P < 0.01 (**). The significant panelist effect suggests the panelists 
were using different parts of the scale. It is important to determine if the 
panelists were scoring the samples consistently, that is, in the same order. 

An analysis of variance with replication allows the sensory analyst to 
test for a panelist by treatment interaction. The absence of an interaction 
indicates the panelists are in agreement. To examine interactions in the 
data the following subtotals are required (Table 8). 



41 



Table 8 Treatment totals for each panelist 







Treatment 






Panelist 


X 


A 


B 


C 


1 


21.2 


24.0 


27.5 


18.6 


2 


21.0 


23.0 


28.0 


23.3 


3 


21.1 


21.3 


25.5 


19.4 


4 


19.6 


21.8 


27.1 


17.6 


5 


17.9 


19.7 


23.3 


14.2 


6 


22.0 


21.6 


27.5 


20.1 


7 


18.4 


21.7 


23.8 


14.2 


8 


20.0 


20.6 


25.2 


14.3 



Sum of squares (treatment by panelist interaction): 

SS(Tr x P) = (Sum of squares of the treatment totals for each 

panelist/number of replications) - SS(P) - SS(Tr) - CF 

= [(21.2 2 + 21.0 2 + 21. I 2 + ... + 14.2 2 + 14.3 2 )/31 - 

29.82 - 96.81 - 4880.63 
= 5019.63 - 29.82 - 96.81 - 4880.63 
= 12.37 
Degrees of freedom (treatment by panelist interaction): 

df(Tr x P) = df(Tr) x df(P) 
= 3x7 
= 21 

The interaction can then be added to the analysis of variance table. The 
sum of squares and degrees of freedom for error are as follows: 

Sum of squares (error): 

SS(E) = SS(T) - SS(Tr) - SS(P) - SS(R) - SS(Tr x P) 
= 188.30 - 96.81 - 29.82 - 10.73 - 12.37 
= 38.57 

Degrees of freedom (error): 

df(E) = df(T) - df(Tr) - df(P) - df(R) - df(Tr x P) 
= 95-3-7-2-21 
= 62 

The replicate, treatment, panelist, and treatment by panelist 
interaction mean squares are now tested with the new error mean square 
(Table 9). 



42 



Table 9 Analysis of variance with replication of apple juiciness 



Source of variation 



df 



SS 



MS 



Replicates 


2 


10.73 


5.37 


8.7** 


Panelists 


7 


29.82 


4.26 


6.9** 


Treatments 


3 


96.81 


32.27 


52.0** 


Treatments x Panelists 


21 


12.37 


0.59 


1.0 


Error 


62 


38.57 


0.62 




**P < 0.01. 











The treatment by panelist interaction was not significant. We conclude 
that the panelists were in agreement. If this were not the case the panelists 
who do not agree are most easily spotted by plotting the treatment totals 
for each panelist against the treatment levels (Fig. 6). Inconsistent 
panelists will stand out as their scores will not be parallel to those of the 
other panelists. 




Fig. 6 Juiciness scores for panelists 1 to 8. 



43 



It is also possible to examine the replicate by treatment interaction and 
the replicate by panelist interaction in a similar fashion. A significant 
replicate by panelist interaction would indicate that some panelists were 
using different parts of the scale from replicate to replicate and this is not 
expected with a well-trained panel. A significant replicate by treatment 
interaction may indicate either that treatment effects vary over replicates 
or that the samples given to the different panelists are not independent. 
This could occur, for example, if all panelists were sampling from the same 
roasts. If this term is significant, the appropriate error term for testing 
treatment effects would be the replication by treatment interaction rather 
than SS(E), as SS(E) may underestimate the error. If not significant, it can 
be pooled with SS(E) as in the above analysis of variance. This technique of 
calculating interaction terms can also be used to calculate treatment A by 
treatment B interactions. For further discussion of interactions and 
choosing appropriate error terms see O'Mahony (1986). When any of these 
interactions are significant, give careful consideration to the 
interpretation of the data. To check treatment by replicate interaction, use 
the replication totals for each treatment as follows: 

Sum of squares (treatment by replicate): 

SS(Tr x R) = (Sum of squares of the treatment totals for each 

replicate / number of panelists) - SS(Tr) - SS(R) - CF 

= [(60.9 2 + 49.5 2 + 50.8 2 + ... + 46.3 2 )/8] - 96.81 - 
10.73 - 4880.63 

= 4992.69 - 96.81 - 10.73 - 4880.63 

= 4.52 

Degrees of freedom (treatment by replicate): 

dftTr x R) = df(Tr) x df(R) 
= 3x2 
= 6 

Mean square (treatment by replicate): 

MS(Tr x R) = SS(Tr x R)/df(Tr x R) 
= 4.52/6 
= 0.75 

To test this MS, the error MS must be calculated once again: 

SS(E) = previous SS(E) - SS(Tr x R) 
= 38.57-4.52 
= 34.05 

df(E) = previous df(E) - df(Tr x R) 
= 62-6 
= 56 

MS(E) - SS(E)/df(E) 
= 34.05/56 
= 0.61 



44 



Calculate the F value for (Tr x R) : 

F(Tr x R) = MS(Tr x R)/MS(E) 
= 0.75/0.61 
= 1.2 

This F value with 6 degrees of freedom in the numerator and 56 degrees 
of freedom in the denominator is not greater than 2.3 (Statistical Chart 9 in 
Appendixes). Thus the treatment by replicate mean square is not 
significant and the previous analysis of variance is appropriate. If 
statistical software were used, you could include any interactions of 
interest in the analysis. Care must be taken to choose the correct error 
term. 

Dunnett's test 

The analysis of variance indicated a significant difference in the juiciness of 
the four treatments of apples. Variety X is the control treatment and the 
sensory analyst wishes to see if treatments A, B, and C differ from X. In the 
case where we wish to compare several treatments with a control, 
Dunnett's test is appropriate. This test can be either two tailed (e.g., are the 
other treatments different with respect to juiciness) or one tailed (e.g., are 
the other treatments juicier). For further discussion of one-tailed and 
two-tailed testing refer to O'Mahony (1986). In this case, we will use a 
one-tailed test. Calculations are very similar to Tukey's but a different 
table is used. 

The standard error of the treatment means is calculated. 



SEM = yO.62/24 
= n/0.026 
= 0.16 

The value from Statistical Chart 10 (Appendix), for four treatments 
(three excluding the control) and 60 degrees of freedom, is 2.10 (P = 0.05). 

Calculate the least significant difference for P = 0.05 by multiplying 
the value obtained from the table by the square root of two and the SEM: 

LSD (0.05) = 2.10 X /2 X 0.16 
= 0.48 

Arrange sample means for treatments other than the control according to 
magnitude: 

X C A B 

6.72 5.90 7.24 8.66 

Compare each treatment mean with the control to see if it scored 
significantly more than the control. If the treatment scored 0.48 or more 
than the control it is significantly juicier at P < 0.05. 



45 



C - X = 5.90 - 6.72 = -0.82 < 0.48 
A - X = 7.24 - 6.72 - 0.52 > 0.48 
B - X = 8.66 - 6.72 = 1.94 > 0.48 

The results can be shown as follows: 

X C A B 

6.7 5.9 7.2* 8.7* 

Thus we conclude that varieties A and B were juicier than the standard 
variety X at P < 0.05 (*). 

Ratio scaling 

Ratio scales are commonly used in physics. Scales of weight and distances 
are examples. A distance of 40 km is twice as long as a distance of 20 km. 
Ratios of measurements can be calculated. Ratio scaling is also used in 
sensory analysis. The ratio measurements are usually constructed by a 
procedure called magnitude estimation (Moskowitz 1988a). Panelists are 
given the samples arranged in random order that vary in one 
characteristic, such as hardness. They are instructed to assign any number 
to the first sample and to rate each sample in relation to the first. If the 
second sample seems twice as hard as the first, and if the first sample were 
assigned 50, the panelist would assign it the value 100; if it seems half as 
hard, it would be rated at 25. 

Magnitude estimation is most appropriate for evaluating a quantity 
that does not include values near the threshold. Transform magnitude 
estimation data to logarithms before carrying out the appropriate analysis 
of variance (Butler et al. 1987). Because one cannot take the logarithm of 
zero, zero values pose a problem. However, if none of the products are near 
the threshold, zeros are unlikely If zeros occur, a small constant may be 
added to all scores (Steel and Torrie 1980). A sample of the questionnaire 
and an example of magnitude estimation follow. 



46 




QUESTIONNAIRE FOR MAGNITUDE ESTIMATION 

PRODUCT: Gelatin 

NAME DATE 



Please evaluate these samples of gel for hardness. Giving the first sample a 
value, assign relative values to each of the other samples to reflect their 
ratio to that of the first sample. 

Samples Hardness 

649 

872 

259 

138 



Comments: 



Example Magnitude estimation was used to find out if there was a 
difference in hardness of several samples of gel made with different 
amounts of gelatin (Table 10). Logarithms (natural) were taken and totals 
and means found (Table 11). 



Table 10 Magnitude estimation scores of gel samples 







Treatment 






Panelist 


1 


2 


3 


4 




(649) 


(872) 


(259) 


(138) 


1 


50 


100 


150 


200 


2 


150 


400 


600 


700 


3 


100 


200 


300 


400 


4 


75 


75 


90 


100 


5 


6 


8 


10 


11 


6 


100 


150 


200 


300 


7 


150 


100 


200 


300 


8 


50 


70 


85 


100 


9 


30 


60 


100 


120 


10 


50 


60 


100 


125 



47 



Table 11 Magnitude estimates as logarithms 







Treatments 






Panelist 


1 


2 


3 


4 


Total 




(649) 


(872) 


(259) 


(138) 




1 


3.912 


4.605 


5.011 


5.298 


18.826 


2 


5.011 


5.991 


6.397 


6.551 


23.950 


3 


4.605 


5.298 


5.704 


5.991 


21.598 


4 


4.317 


4.317 


4.500 


4.605 


17.739 


5 


1.792 


2.079 


2.303 


2.398 


8.572 


6 


4.605 


5.011 


5.298 


5.704 


20.618 


7 


5.011 


4.605 


5.298 


5.704 


20.618 


8 


3.912 


4.248 


4.443 


4.605 


17.208 


9 


3.401 


4.094 


4.605 


4.787 


16.887 


10 


3.912 


4.094 


4.605 


4.828 


17.439 


Total 


40.478 


44.342 


48.164 


50.471 


183.455 


Mean 


4.048 


4.434 


4.816 


5.047 


18.346 



Analysis of variance 

NOTE: Readers not familiar with the analysis of variance 
procedure should refer to the complete description given under 
"Unstructured scaling." 

Correction factor: 

CF = 183.455 2 /40 
= 841.393 

Sum of squares (treatment): 

SS(Tr) = (40.478 2 + 44.342 2 + ... + 50.471 2 )/10 - CF 

= 8471.77/10 - CF 

= 847.177-841.393 

= 5.784 

Sum of squares (panelists): 

SS(P) = (18.826 2 + 23.950 2 + ... + 17.439 2 )/4 - CF 

= 3518.254/4 - CF 

= 879.564-841.393 

= 38.171 

Sum of squares (total): 

SS(T) = (3.912 2 + 5.011 2 + ... + 4.828 2 ) - CF 
= 886.713-841.393 
- 45.320 

The analysis of variance is summarized in Table 12. 



48 



Table 12 Analysis of 


variance 


ofg< 


*1 firmness 






Source of variation 


df 




SS 


MS 


F 


Treatment 

Panelists 

Error 


3 

9 

27 




5.784 

38.171 

1.365 


1.928 
4.241 
0.051 


37.8** 
83.2** 



**P < 0.01. 



The F-value for treatment is 37.8. According to Statistical Chart 9 
(Appendix), if the F value exceeds 2.96 there is a significant difference at 
P < 0.05 (*); if it exceeds 4.40 there is a significant difference at P < 0.01 

In this example the treatment levels were four ordered levels; 20, 25, 
30, and 35 g of gelatin added to 800 mL of water or on the logarithmic scale 
2.996, 3.219, 3.401, and 3.555. When the treatments are ordered levels it is 
often appropriate to look at a regression of the means on the treatment 
levels. In magnitude estimation, it has been postulated (Stevens 1956) that 
the treatments and levels are related as follows: 

log Y = oc %\- p log X + e 

where Y is the treatment mean 
X is the treatment level 
e is the error 
oc&nd (3 are to be estimated. 

To examine the linear regression of log Y on log X one proceeds on the 
logarithmic scale as follows. 

Numerator correction factor The numerator correction factor (NCF) is 
the product of the sum of the treatment means and the sum of the 
treatment levels means all divided by the number of treatment levels. 

NCF = [(4.048 + 4.434 + 4.816 + 5.047) X (2.996 + 3.219 + 
3.401 + 3.555)]/4 

= (18.345 x 13.17D/4 

= 241.6220/4 

= 60.4055 

Numerator The numerator (NUM) is the sum of the cross product of 
treatment levels and treatment means minus the correction factor 
numerator, all multiplied by the number of panelists. 

NUM = [(2.996 X 4.048) 4- (3.219 X 4.434) + (3.401 X 4.816) + 
(3.555 X 5.047) - NCF] x 10 
= [60.7222 - 60.4055] X 10 
= 0.3167 x 10 
= 3.167 



49 



Denominator correction factor The denominator correction factor (DCF) 
is the square of the sum of the treatment levels divided by the number of 
treatment levels. 

DCF = (2.996 + 3.219 + 3.401 + 3.555) 2 /4 

= 13.171 2 /4 

= 173.4752/4 

= 43.3688 

Denominator The denominator (DEN) is the sum of squares of the 
treatment levels minus the denominator correction factor all multiplied by 
the number of panelists. 

DEN = K2.996 2 + 3.219 2 + 3.401 2 + 3.555 2 ) - DCF] x 10 

= [8.9760 + 10.3620 + 11.5668 + 12.6380-43.3688] x 10 

= 0.1740 X 10 

= 1.740 

Slope The slope ((3) is the numerator divided by the denominator, 

NUM/DEN. 

(3 = 3.167/1.740 
= 1.82 

Intercept The intercept ( oc % is the sum of the treatment means minus the 

slope times the sum of the treatment levels all divided by the number of 
levels. 

oc*= (18.346-1.82 x 13.17D/4 
= (18.346 - 23.97D/4 
= -5.625/4 
= -1.41 

Sum of squares (regression) The sum of squares for regression SS(R) is 
the numerator squared divided by the denominator. 

SS(R) = NUM7DEN 
= 3.16771.74 
= 5.764 

Sum of squares (deviation from regression) The sum of squares for 
deviation from regression (SS(D)) is the sum of squares for treatment 
minus sum of squares for regression. 

SS(D) = SS(Tr) - SS(R) 
= 5.784-5.764 
= 0.020 

The analysis of variance can then be summarized as in Table 13. 



50 



Table 13 Analysis of variance of gel hardness 



Source of variation 



df 



SS 



MS 



Treatments 


3 


5.784 


1.928 


37.8** 


Regression log/log 


(1) 


5.764 


5.764 


113.0** 


Deviation from regression 


(2) 


0.020 


0.010 


0.2 


Panelists 


9 


38.171 


4.241 


83.2** 


Error 


27 


1.365 


0.051 





**P < 0.01. 



The F value of 113 for the regression of the log treatment effects on the 
log solution levels strongly indicates a linear effect on the log scale. The 
deviation from this line is nonsignificant indicating that the line fits very 
well (Fig. 7). The equation for the line is 

logY = -1.41 + 1.82 log X + e 

This procedure is not limited to magnitude estimation but can be used 
whenever a linear relationship is postulated between the treatment scores 
and treatment levels. If the levels are equally spaced, the computations can 
be simplified by the use of orthogonal polynomials (Steel and T orrie 1980) . 



5.15i 



5.05- 
4.95- 
£ 4.85- 
.i 4.75 
4.65- 
4.55- 



0) 

■D 

13 



l 

E 



O 



4.35 
4.25- 
4.15- 
4.05- 



3.95 



2.9 



3.5 



3 3.1 3.2 3.3 3.4 

Log treatment level 

Fig. 7 Logarithm of the magnitude estimates plotted against logarithm of the 
treatment levels. 



51 



For more complicated relationships the reader is directed to Cochran and 
Cox (1957). Often a graph will be the best presentation of the results. 

Descriptive analysis methods 

The scaling tests described can be used to evaluate just one or several 
sensory characteristics of a product. Methods of descriptive analysis have 
been developed, which can be used to generate a more complete description 
or profile of the sensory quality of a product. Three such methods are the 
flavor profile, texture profile, and quantitative descriptive analysis. 

Flavor profiling 

The flavor profile method was introduced by Arthur D. Little Co., 
Cambridge, Massachusetts, in 1949 (Cairncross and Sjostrom 1950; Caul 
1957). The method provides a detailed, descriptive analysis of a product's 
flavor characteristics in both quantitative and qualitative terms. Trained 
panelists are used to analyze and discuss the flavor characteristics of a 
product in an open session approach to achieve a consensus. The final 
profile describes a product's aroma and flavor in terms of its detectable 
factors, their intensities, and their order of detection, any aftertaste, and 
an overall impression. The selection of panelists is based on taste and 
olfactory discrimination and descriptive ability (see "Selection and 
training of panelists"). During the long training process, panelists are 
trained in the fundamentals of the flavor profile method and in the physical 
and psychological aspects of tasting and smelling. They are presented with 
a wide selection of reference standards representing the product range, as 
well as samples to demonstrate ingredient and processing variables, to help 
develop and define the terminology that they will use. 

During an actual flavor profiling session, four to six trained panelists 
sit around a table. The panelists first analyze the product or products 
individually, and then discuss their evaluations as a group. The products are 
analyzed one at a time for aroma, flavor, and mouth feelings, which are all 
called "character notes," using a degree of intensity scale that uses the 
following fairly broad demarcations: 

= not present 
)( = threshold 

1 or + = slight 

2 or + + = moderate 

3 or + + + = strong 

In some instances, for example, when they compare two very similar 
products, panelists can designate narrower ranges by using such symbols 
as 1/2, + (plus), or - (minus) (Caul 1957). The order of appearance of these 
character notes is indicated along with any aftertaste perceived. 



52 



An indication of the overall amplitude or impression of the aroma and 
flavor is given using the following scale: 

)( = very low 

1 = low 

2 = medium 

3 = high 

Because the final flavor profile of the product is a group consensus, no 
statistical analysis on the intensity values can be carried out. To 
circumvent this limitation, category scales or line scales can be used in 
place of the conventional 0, )(, 1, 2, 3 scale, and the panelists can make 
individual judgments rather than obtaining a group consensus. 

An example of a scoresheet, which might be used in profiling the flavor 
of beer, follows. 




QUESTIONNAIRE FOR FLAVOR PROFILE 



PRODUCT: Beer 

NAME 



DATE 



Comments: 



AROMA 

Amplitude 

Hoppy 

Fruity 

Sour 

Yeasty 

Malty 

FLAVOR 

Amplitude 

Tingly (carbonation) 

Sweet 

Fruity 

Bitter 

Malty 

Yeasty 

Metallic 

Astringent 

AFTERTASTE 



Intensity 



Intensity 



53 



During the group discussion, the panelists must reach a unanimous 
decision on the product evaluation. The panel leader then consolidates the 
panelists' conclusions into a concise description or flavor profile of the 
product. 

Flavor profiles are often illustrated using a semicircular diagram 
(Fig. 8). The semicircle denotes the threshold concentrations, with the 
radiating lines corresponding to each individual character note (in order of 
appearance) and the length of the lines representing the intensity ratings 
(Cairncross and Sjostrom 1950). 



Sour 



Yeasty 




Malty 



Fig. 8 Diagrammatic representation of the aroma portion of a beer sample 
flavor profile. 



Texture profiling 

The texture profile method was developed at the General Foods Research 
Center by Margaret Brandt and Alina Szczesniak (Brandt et al. 1963; 
Szczesniak 1963). This method classifies the textural parameters of a food 
not only into mechanical and geometrical qualities, but also into properties 
related to fat and moisture content. A quantitative and qualitative 
description is obtained with information on the intensity of each textural 
parameter present and the order in which they appear from the first bite 
through to complete mastication. 

The selection of panelists is based on their textural discrimination and 
their descriptive ability. During training, panelists are introduced to the 
principles of texture as related to the structure of food. Through exposure 
to a wide range of food products, they are provided with a wide frame of 
reference for textural characteristics (Civille and Szczesniak 1973). 
Szczesniak and colleagues (1963) developed rating scales for different 
textural characteristics, which are useful during the panel training process. 



54 



The scales illustrate hardness, fracturability, chewiness, adhesiveness, and 
viscosity and include reference standards for each point on the scale. The 
reference foods are standardized with respect to brand name, handling 
procedure, sample size, and temperature. Substitutions of a reference food 
maybe made, as long as the new food is a major brand of good consistency, 
requires minimum preparation to eliminate possible sources of variation, 
and does not change drastically with small temperature variations. Table 
14 shows an example of the hardness scale. 

Table 14 Standard hardness scale 



Scale 










value 


Product 


Brand or type 


Sample size 


Temperature 


1 


Cream cheese 


Kraft Philadelphia 


1.5 cm cube 


7-13°C 


2 


Egg white 


Hard-cooked 
(5 min) 


1.5 cm of tip 


20-25 °C 


3 


Frankfurters 


Schneiders, large 


1.5 cm slice 


10-18°C 


4 


Cheese 


Kraft mild Cheddar 


1.5 cm cube 


10-18°C 


5 


Olives 


McLaren's, stuffed, 


1 olive, 








queen-size 


pimento removed 


10-18°C 


6 


Peanuts 


Cocktail-type 


1 nut 


20-25 °C 


7 


Carrots 


Uncooked, fresh 


1.5 cm slice 


20-25 °C 


8 


Almonds 


McNair, unblanched 


1 nut 


20-25 °C 


9 


Humbugs 


McCormick 


1 


20-25 °C 



Source: adapted from Szczesniak et al. (1963). 



Each scale encompasses the entire range of intensity of the textural 
characteristic encountered in foods. The scale is first introduced in its 
entirety to familiarize the panelists with the specific texture parameter. 
Then the portion of the scale that corresponds to the extremes of the 
texture parameter of the test product or products is identified and 
expanded. The original texture profile method used an expanded 14-point 
version of the flavor profile scale. More recently, however, structured or 
unstructured scales, or magnitude estimation has been used. For example, 
the hardness of three new wieners is to be evaluated. Three points on the 
scale, 2 (egg white), 3 (frankfurters), and 4 (cheese), encompass the 
extremes in hardness of the three new test wieners. The three-point scale 
can be expanded by establishing reference points using wiener products 
between the two extreme points of egg white and cheese. This procedure is 
repeated for each texture attribute present in the product. 

Originally, the texture profile method involved a group discussion and 
panel consensus as for the flavor profile method. However, now it is more 
common to have panelists evaluate the samples individually for each 
texture characteristic present using the developed scales to allow for 
statistical analysis of the data. 



55 



Quantitative descriptive analysis 

A method of sensory analysis called quantitative descriptive analysis 
(QDA) was developed at the Stanford Research Institute (Stone et al. 1974) 
by which trained individuals identify and quantify the sensory properties of 
a product in order of occurrence. The basic features of the method are as 
follows: 

• development of the sensory language as a group process 

• panelist selection based on performance with test products 

• as many as 12-16 repeat judgments from each panelist 

• individual evaluations in booths 

• unstructured scales 

• analysis of variance to analyze individual and panel performance 

• correlation coefficients to determine relationships among various scales 

• statistical analysis to determine primary sensory variables 

• multidimensional model developed and related to consumer responses. 

An example of the attributes that might arise from QDA of orange jelly 
is shown in Table 15. 

The type of visual display in Fig. 9 was suggested by Stone et al. (1974). 
The distance from the centre point to each attributes' point is the mean 
value of that attribute for each product. Standard errors could be included 
on the diagram. 

Table 15 Results of analysis of variance 1 of orange jelly using quantitative 
descriptive analysis 



Attribute 


Brand A 


Brand B 


SEM 2 


Probability 3 


Orange color 


10.2 


7.9 


0.62 


0.011 


Orange aroma 


7.6 


6.9 


0.50 


0.325 


Firmness 


9.6 


6.6 


0.64 


0.001 


Tartness 


8.6 


6.9 


0.66 


0.072 


Orange flavor 


7.6 


6.9 


0.72 


0.494 


Foreign flavor 


4.3 


4.8 


0.48 


0.464 


Sweetness 


7.1 


9.6 


0.42 


< 0.001 


Rate of breakdown 


5.1 


6.1 


0.60 


0.242 



1 Means based on 50 observations; 5 replicates of 10 panelists. 
; Standard error of the mean based on 76 degrees of freedom. 
3 Probability that Brand A has the same intensity as Brand B. 



56 



Firmness 



Tartness ^ 

Orange aroma 




Orange// \ \ Orange 

flavor S\ • / ^ C oior 



Foreign flavor 

Rate of breakdown 



Product A 

Sweetness Product B 

Fig. 9 Graphical representation of the orange jelly data. 

Food Research Centre panel 

Descriptive analysis at the Food Research Centre uses a form of attribute 
analysis for panel training and test product analysis. The following 
example outlines a panel procedure to analyze white sauces made with 
varying levels of a new, enriched flour. The objective is to examine the effect 
of flour substitution on the sensory quality of the sauce. 

First, test several formulations to determine the best formulation for 
the control or standard white sauce and at the same time to standardize the 
cooking procedure. Once you have chosen the formulation, make sauces 
substituting varying levels of the new flour for the original flour; in this way 
determine if there is a maximum level for flour substitution based on 
physical performance. For example, at one substitution level the sauce 
might not thicken. Let us assume that after 25% substitution, the new flour 
does not allow the sauce to thicken. Therefore, the levels of new flour 
substitution to be examined are set at 0, 5, 15, and 25%. Once sample 
preparation is standardized, panel training can start. 

During the first training session present the panelists with a control 
sauce (0% new flour substitution) and the 25% new flour sauce. Ask them to 
compare the sensory properties of the two samples and write down any 
differences and similarities on a blank piece of paper. The evaluations are 
done individually. After the session, the panel leader compares the 



57 



responses and groups similar comments together, usually in the order of 
perception (i.e., visual, aroma, mouthfeel, taste/flavor, and aftertaste). For 
example, all the comments relating to visual properties are grouped 
together. 

The next day, present the panelists with a list of all their comments 
from the previous day and any additional suggested terms from the panel 
leader. Then ask them to compare the control and 25% sauce again and, 
working with the list of provided comments as possible descriptors, to 
describe the differences and similarities between the two sauces. The 
panelists can add descriptors that are not on the list. Again, this evaluation 
is done individually. The panel leader then compares the comments and 
identifies any sensory descriptors commonly used amongst the panelists. 
These descriptors are the ones to be focused on during further training. 

At the third training session, the panelists start working with the first 
grouping of sensory comments, in this case the visual descriptors. Present 
them with three sauces, a control, 5%, and 25%. Again using the list 
provided, the panelists make individual evaluations of the sauces. After 
each panelist has completed the evaluation, they discuss the observations 
as a group. Each descriptor is discussed separately with the hope of 
achieving agreement among the panelists as to which sample has the lowest 
and highest degree of that sensory characteristic. For example, if yellow 
color was a descriptor, the panel leader would try to establish consensus 
among the panelists as to which sauce was the most yellow, the least yellow 
and which is in between. The same procedure would take place for each 
sensory characteristic identified. Any characteristic that is noted by less 
than 50% of the panelists, during round-table discussions is dropped from 
the list if the panel leader agrees it is inappropriate. Otherwise, further 
training is needed to help the nonusers. 

In preparation for the next day of training, the panel leader draws up a 
training ballot with a scale for each descriptor discussed the previous day. 
Examples are supplied to the panelists for any sensory characteristic for 
which a consensus was not reached. For example, Munsell color chips are 
useful color standards. The panelists discuss the standards and evaluate 
the test samples for each sensory characteristic on the ballot, followed by a 
group discussion of the samples. Once agreement is reached among 
panelists about the visual characteristics of the samples, the training 
moves on to the next grouping of sensory comments, in this case aroma. 

Training for the aroma characteristics proceeds the same as described 
for the visual characteristics. Remember, during training the method of 
sample evaluation is also determined. For example, the aroma is to be 
evaluated by lifting the lid of the sauce container, taking three short sniffs, 
and then replacing the lid on the container. The lid is replaced to allow for 
headspace saturation in case the panelist wants to reevaluate a sample. 
Examples of problem descriptors are again supplied to help panelists to 
achieve consensus. One can use actual examples of the identified aroma, 
such as earth for an "earthy" aroma, or chemicals known to elicit certain 
perceived character notes, such as isopropyl quinoline for an "earthy" 



58 



aroma. A useful guide to odorant chemicals is the Atlas of odor character 
profiles by A. Dravnieks (1985). 

The next training sessions would focus on mouthfeel properties. By 
now the panelists are more familiar with the test samples, so you can 
include the fourth or 15% new flour substitution sample. Again, address 
and standardize the sample evaluation procedure. For example, 
standardize both the use of a different spoon for each sauce and the amount 
of sample taken into the mouth. A reference for texture terminology 
examples, which could be useful for panel training is Munoz 1986. 

Flavor would be the last grouping for which to train. When supplying 
samples to illustrate descriptors, keep in mind the preparation procedure 
of the test samples. For example, if "celery" is one of the descriptors 
panelists have identified, then the decision might be to supply both raw and 
cooked celery to the panelists because the sauce is cooked. 

Once the panelists have been trained on all the appropriate sensory 
properties, the final scoresheet is put together by the panel leader. The 
order of appearance of each sensory characteristic on the scoresheet 
should be based on the order of perception and the logistics of evaluation. 
For example, although the panelists were trained on visual characteristics 
first, the aroma descriptors should appear first on the scoresheet owing to 
the importance of sample temperature and headspace saturation for aroma 
evaluation. An example of the final questionnaire follows. 



59 







QUESTIONNAIRE FOR WHITE SAUCE 




NAME. 



DATE 



Please evaluate the samples in the following order: 

361 478 952 660 
Aroma: 
1) Earthy 



slight 
Color: 
2) Yellow 



intense 



slight 

Mouth feel: 
3) Grainy 



intense 



slight 
4) Consistency 



very 



thin 

Flavor: 
5) Buttery 



thick 



slight 



6) Salty 



intense 



slight 
7) Celery 



very 



slight 
Comments: 



very 



60 



This questionnaire is now tested. The panelists evaluate the test 
samples as if in a real test session. After the individual evaluations, the 
panelists discuss the samples and the evaluation procedure. For example: 
Are four samples too many? Are the descriptors in the correct order for 
evaluation? Are the appropriate words used for anchor points on the 
scales? At the same time, panelists are tested to see if they can reproduce 
their judgments. The reader is directed to American Meat Science 
Association (1978). Any necessary changes are made and retested before 
the real test sessions start. 

After sufficient replication, the data are entered into the computer to 
be used for statistical analysis. Because the data are analyzed by computer, 
it is important to check for any errors in the data values that would more 
easily be detected were calculations done by hand. For each variable, 
maximums, minimums, means, and variances for each treatment, 
replicate, and panelist are examined. A careful examination of these helps 
us to detect any unusual values or problems in the data. For example, if one 
treatment has a very large or small variance we would not want to proceed 
to an analysis of variance which assumes variances are similar for all 
treatments. Plots of the data are also very useful at this stage. Once we are 
satisfied the data are in good order, the data are analyzed by the 
appropriate statistical method using a computer where possible. A report is 
prepared. 



Affective tests 



Affective tests are used to measure subjective attitudes towards a product 
based on its sensory properties. Test results give an indication of 
preference (select one over another), liking (degree of like/dislike), or 
acceptance (accept or reject) of a product (Pangborn 1980). The tests are 
generally used with a large number of untrained respondents to obtain an 
indication of the appeal of one product versus another. 

Affective testing usually follows discriminative and descriptive testing, 
during which the number of product alternatives have been reduced to a 
limited subset. Stone and Sidel (1985) refer to the three primary types of 
affective tests as laboratory, central location, and home placement and 
suggest response numbers of 25-50, >100, and 50-100, respectively. The 
panelists are often selected to represent target markets. 

Affective testing in the laboratory is used as part of the product 
screening effort to minimize testing of products that do not warrant 
further consideration. The laboratory panel can give an indication of 
product acceptability and provide direction for choosing products for the 
larger central location or home placement test. Three frequently used 
methods of affective testing are paired comparison, hedonic scaling, and 
ranking. 



61 



Paired comparison preference test 

The paired comparison test used in preference testing is similar to that 
used in discriminative testing. The test requires the panelist to indicate 
which of two coded samples is preferred. Including a "no preference" or a 
"dislike both equally" option on the ballot is recommended only with a 
panel size of greater than 50 respondents (Gridgeman 1959; Stone and 
Sidel 1985). Permitting a tie with a small panel size reduces the statistical 
power of the test (i.e., reduces the probability of finding a difference 
between samples). Panelists are always concerned about making the right 
choice. They will often fall back on the "no preference" option, if it is 
included. Therefore, usually the panelists are asked to choose one sample, 
even if they perceive both samples as being the same, keeping the test as a 
forced choice test. 

Two coded samples (A and B) are served simultaneously, with identical 
presentation style, i.e., same sample size, temperature, and container. 
There are two possible orders of presentation; A-B or B-A. Use each order 
an equal number of times for a small panel or select the order at random for 
a large panel. The order in which the panelist is to evaluate the samples is 
indicated on the ballot. Panelists usually evaluate only one pair of samples 
in a test with no replication. They are allowed to retaste the samples. 

The researcher must decide if the test is a one- or two-tailed test. If the 
objective is to confirm a definite "improvement" or treatment effect on 
sample preference, then it is a one-tailed test. If the objective is to find 
which of two samples is preferred without any preconceived outcome, the 
test is a two-tailed test. The total number of panelists preferring each 
sample is calculated and tested for significance according to Statistical 
Chart 3 or 4 (Appendix). (See "Paired comparison test" for instructions on 
how to use the chart.) Although test results might indicate a preference for 
one sample over another, they give no data on the size of the difference in 
preference between the samples or on what the preference was based. 

A sample questionnaire and an example of a paired comparison 
preference test follow. 



62 



QUESTIONNAIRE FOR PAIRED COMPARISON 
PREFERENCE TEST 



PRODUCT: Cookies 

NAME 



DATE 



Taste the two cookies in the following order: 

256 697 

Which cookie do you prefer? You must make a choice. 



Comments: 



Example A paired comparison preference test was used to determine 
which of two chocolate-chip cookies was preferred (Fig. 10). Fifty panelists 
compared the two cookies. Twenty-five panelists evaluated a cookie from 
treatment A first, whereas the other 25 evaluated a cookie from treatment 
B first. 




Fig. 10 Tray prepared for a paired comparison preference test. 



63 



Thirty-five of the 50 panelists preferred the cookies from treatment B. 
According to Statistical Chart 3 (Appendix), the probability is 0.007, which 
is less than the critical value of 0.05. The conclusion is that the cookie from 
treatment B was preferred by the panelists. 

Hedonic scaling test 

The most commonly used test for measuring the degree of liking of a 
sample is the hedonic scale. The term "hedonic" is defined as "having to do 
with pleasure." The scale includes a series of statements or points by which 
the panelist expresses a degree of liking or disliking for a sample. Scales of 
varying lengths can be used, but the most common is the 9-point hedonic 
scale, ranging from "like extremely" to "dislike extremely" with a central 
point of "neither like nor dislike" (Peryam and Girardot 1952). 

The samples are coded and served in identical presentation style. The 
order of sample presentation is randomized for each panelist, and the order 
is indicated on the ballot. The samples can be served simultaneously or one 
at a time. 

The responses are converted to numerical values ranging from 1 for 
"dislike extremely" to 9 for "like extremely" The data are analyzed either 
by t-test if only two samples are evaluated or by analysis of variance if three 
or more samples are evaluated. For a discussion of the appropriateness of 
the t-test and analysis of variance see "Structured scaling." An alternate 
analysis would be to rank the scores for panelists and conduct a Friedman's 
test (see "Ranking" under "Discriminitive tests"). 

A sample questionnaire and example of the 9-point hedonic scale 
follow. 



64 



QUESTIONNAIRE FOR HEDONIC SCALE 



PRODUCT: Cottage cheese 

NAME 



.DATE 



Please evaluate the 
Indicate how much 
appropriate phrase. 

216 

like extremely 

Jike very much 

like moderately 

like slightly _ 



four cottage cheese samples in the following order, 
you like or dislike each sample by checking the 



709 

Jike extremely 
Jike very much 
Jike moderately 
Jike slightly 



511 

Jike extremely 
Jike very much 
Jike moderately 
Jike slightly 



124 

Jike extremely 
Jike very much 
Jike moderately 
Jike slightly 



neither like 


neither like 


neither like 


neither like 


nor dislike 


nor dislike 


nor dislike 


nor dislike 


dislike slightly 


dislike slightly 


dislike slightly 


dislike slightly 


dislike moderately 


dislike moderately 


dislike moderately 


dislike moderately 


dislike very much 


dislike very much 


dislike very much 


dislike very much 


dislike extremely 


dislike extremely 


dislike extremely 


dislike extremely 


Comments: 









Example A 9-point hedonic scale was used to determine which brand of 
cottage cheese was most liked. Forty-one panelists evaluated the four 
samples. The data (Table 16) were submitted to analysis of variance (Table 
17) to test for significance and Tukey's test was used to compare sample 
means (Table 18). (See "Unstructured scaling" for statistical analysis.) 



65 



Table 16 Hedonic scores for the four brands of cottage cheese 



Panelist 




Brand 




Panelist 




Brand 






A 


B 


C 


D 


A 


B 


C 


D 


1 


4 


6 


7 


3 


21 


7 


8 


6 


3 


2 


5 


6 


8 


5 


22 


9 


6 


6 


3 


3 


8 


7 


8 


2 


23 


4 


4 


8 


5 


4 


8 


9 


9 


7 


24 


4 


8 


8 


4 


5 


2 


7 


2 


1 


25 


7 


5 


4 


4 


6 


8 


6 


6 


2 


26 


6 


7 


3 


7 


7 


4 


5 


6 


7 


27 


7 


4 


7 


3 


8 


7 


8 


8 


7 


28 


7 


3 


3 


6 


9 


8 


6 


6 


7 


29 


8 


6 


7 


7 


10 


4 


7 


5 


5 


30 


7 


6 


8 


6 


11 


7 


5 


8 


6 


31 


4 


9 


6 


8 


12 


7 


7 


7 


8 


32 


9 


5 


8 


4 


13 


7 


6 


8 


7 


33 


8 


6 


7 


6 


14 


8 


6 


8 


9 


34 


3 


7 


8 


5 


15 


4 


5 


5 


5 


35 


5 


5 


7 


8 


16 


6 


8 


7 


1 


36 


7 


8 


9 


3 


17 


8 


6 


7 


3 


37 


7 


8 


8 


7 


18 


4 


7 


5 


6 


38 


6 


5 


8 


3 


19 


6 


8 


9 


6 


39 


8 


7 


8 


9 


20 


8 


1 


6 


3 


40 


6 


8 


9 


7 












41 


5 


5 


6 


8 



Table 17 Analysis of variance of results of cottage cheese hedonic scales 



Source of variation 



df 



SS 



MS 



Brands 
Panelists 
Error 
Total 



3 


50.39 


16.80 


5.69** 


40 


183.99 


4.60 


1.56* 


120 


354.11 


2.95 




163 


588.49 







* P < 0.05; **P < 0.01. 



66 



Table 18 Means and standard error of the mean (SEM) for the four 
brands of cottage cheese 





Brand mean 






c 


A B 


D 


SEM 


6.8 a 


6.3 a 6.2 ab 


5.3 b 


0.27 



The results indicate that the panelists liked brands C and A 
significantly more than brand D (Tukey's test). The mean scores of 6.8 to 
6.3 for brand C and A, respectively, cover the "like moderately" (score = 7) 
and "like slightly" (score = 6) categories, whereas 5.3 for brand D 
corresponds to the "neither like nor dislike" (score = 5) category. Note that 
the difference between brands B and D is close to significance at P = 0.05. 

Ranking test 

The ranking test requires a panelist to evaluate three or more coded 
samples and to arrange them in ascending or descending order of 
preference or liking. Each sample must be assigned a rank; no ties are 
allowed. The panelist can be asked to rank for overall preference, or to zero 
in on a specific attribute, such as color or flavor preference. 

Code and present the samples in identical style. Randomize the order 
of the samples for each panelist and indicate the order on the ballot. Serve 
the samples simultaneously to allow for any "among"-sample comparison 
necessary to assign ranks. 

Total the ranks for each treatment and test for significance using a 
Friedman test for ranked data. Compare the differences between all 
possible pairs of ranks. (See "Ranking test (Friedman)" under 
"Discriminative tests" for further instructions.) 

Although treatments will be ranked in ascending or descending order 
of preference or liking, the rank values do not indicate the amount or 
degree of difference between treatments. Also, because of the relative 
nature of the rank, values from one set of samples cannot be compared 
directly to another set of samples, unless both sets represent the same 
treatments. A sample questionnaire and example of the ranking test follow. 



67 



QUESTIONNAIRE FOR RANKING TEST 

PRODUCT: Chocolate bars 

NAME DATE 



Please rank these chocolate bars in the order of acceptability. Rank the 
most acceptable chocolate bar as first and the least acceptable as fourth. Do 
not assign the same rank to two samples. 

Evaluate the chocolate bars in the following order: 

551 398 463 821 

Rank Sample code 

Most acceptable First 

Second 

Third 

Least acceptable Fourth 



Comments: 



Example A ranking test was used to determine the order of acceptability 
for four chocolate bars with varying amounts of caramel. Forty panelists 
compared the samples. The rank sum for each chocolate bar is totaled. 

The results are analyzed using the Friedman test for ranked data: 

T = {12/[number of panelists x number of treatments x (number of 
treatments + 1)]} x (sum of the squares of the rank sum of each 
treatment) - 3 (number of panelistsKnumber of treatments + 1) 

[12/(40)(4)(5)][41 2 + 84 2 + 127 2 + 151 2 ] - 3(40X5) 
= 115.01 

The calculated value of Tis 115.01, which is greater than the value of x 2 
with 3 degrees of freedom for a = 0.05, 7.81 (Statistical Chart 6 in 
Appendixes). Therefore we conclude that there is a significant difference in 
acceptability among the samples (P < 0.05). The least significant 
difference is determined using Statistical Chart 7 (Appendix) as described 
earlier (see "Ranking test (Friedman)" under "Discriminative tests"). 

LSD rank = 3.63 /[No. panelists x No. treatments x (No. treatments + l)]/l2 

= 29.6 

Any two treatments where rank sums differ by more than 29.6 are 
significantly different (Table 19). 



68 



Table 19 Rank sum totals for the four chocolate bars 

Chocolate bar Rank sum 1 Average rank 

A 41a 1.0 

B 84b 2.1 

C 127c 3.2 

D 151c 3.8 

1 Rank sums followed by the same letter are not significantly different (P > 0.05). 



The results indicate that chocolate bar A was the most acceptable, 
chocolate bar B ranked second, whereas chocolate bars C and D were the 
least acceptable and did not differ between themselves. 



Sensory analysis report 

In any study or experiment, accurate and complete reporting is essential to 
the eventual usefulness of the results. Any report should contain enough 
detail 

• to allow the reader to understand the study, to judge the appropriateness 
of the procedures, and to evaluate the reliability of the results 

• to allow the study to be repeated 

• to allow intra- and inter-laboratory comparisons to be made (Prell 1976). 

In preparing a report follow these guidelines: title, abstract or 
summary, introduction, experimental method, results and discussion, 
conclusions, and references. For more information and actual examples, 
refer to Prell (1976), Larmond (1981), and Meilgaard et al. (19876). 

Title 

The first information necessary in a report is the title of the project or 
experiment, the names of the persons who are responsible for reporting the 
work, their affiliations, and when the work was done. 

Abstract or summary 

If the report is for publication in a journal, include a short abstract or 
summary, generally of 100-200 words in length (the length is specified by 
the journal). In the abstract, state the objective, provide a concise 
description of the experiment or experiments, and report the major 
observations, the significance of the results, and the conclusions. Even if 
the report is not targeted for publication, a brief summary can be useful to 
the reader, particularly nontechnical readers, such as managers. 



69 



Introduction 

In the introduction, clearly state the aim of the project as well as the 
objective of each test within that project. Define the purpose of the 
investigation or the problem to be solved, e.g., new product development, 
product matching, product improvement, storage stability, and so on. 
Review or cite any pertinent previous work. 

Experimental method 

Under experimental method, describe the sensory procedures and 
statistical analyses used. Give sufficient detail about the method and 
equipment to allow the work to be repeated. Always cite accepted methods 
by appropriate and complete references. The use of subheadings here can 
help to provide clarity, which makes information more useful. Consider the 
following subheadings: 

Experimental design Include here the statistical design used (e.g., 
randomized complete block, incomplete block, or split plot); the 
measurements made (i.e., sensory, chemical, and physical); factors and 
levels of factors; and number of replications. State any limitations to the 
design, such as only certain lots being available for sampling. 

Sensory method Identify the sensory method or methods used and give 
appropriate references, such as the International Organization for 
Standardization (ISO), American Society for Testing and Materials 
(ASTM), or papers from refereed journals. 

Sensory panel State the source of the panel (in-house or recruited from 
outside the organization) and number of panelists. If the panelists were 
trained, give details on the method of selection and training. Information 
on the composition of the panel, such as age and sex, is usually important 
when affective tests are used. 

Environmental conditions Describe the test location (i.e., laboratory, 
shopping mall, or home) and lighting. Include other information, such as 
room temperature or existence of distractions (e.g., odors or noise). 

Sample preparation and presentation Provide details on the equipment 
for, and method or methods of, sample preparation (e.g., electric oven, 
time, and temperature). Specify the use of sample codes (i.e., three-digit 
random numbers), order of presentation, sample size, carrier, 
temperature, container, utensils, time of day, special instructions to 
panelists, time intervals, rinsing agent(s), whether samples were swallowed 
or expectorated, and any other conditions that were controlled or would 
influence the data collected. 

Statistical techniques Describe the manner in which numbers or scores 
were derived from the test responses to enable data analysis. Discuss the 
type of statistical analysis used. 



70 



Results and discussion 

Present results clearly and concisely, summarizing the relevant collected 
data, but giving enough data to justify conclusions. When reporting tests of 
significance, indicate the probability level, degrees of freedom, calculated 
value of the test (F, x 2 , t, etc.), and direction of the effect. Besides words, use 
either tables or figures to present results, but avoid presenting the same 
information twice. Tables can also be used to report analysis of variance 
results, or treatment means and their standard errors. 

Data are often more easily understood and discussed if they can be 
visualized through the use of charts and graphs. Fig. 11 is an example of a 
frequency distribution presented as a bar graph or histogram. If only the 
mean score of 6, corresponding to "like slightly" on the hedonic scale, is 





20 




18 




16 




14 


>> 


12 


o 




c 




CD 


10 


CT 




CD 






8 




4 

2 



2 3 4 5 6 

Hedonic score 

Fig. 11 Example of a histogram. 



8 



71 



reported, one does not see the whole picture. The histogram shows that 
there are actually two different groups of consumers— one group who most 
often rated the product as "dislike slightly," a score of 4, and a second group 
who most often rated the product as "like very much," a score of 8. In this 
case, visualization of the results gives more information than just reporting 
the mean. 

Fig. 12 is an example of results presented in graphical form. A 
10-member trained panel evaluated the perceived intensity of sourness in 
lemonade with varying levels of sucrose added. The mean sourness scores 
are plotted against the sucrose levels. The standard error bars are included 
for an indication of variability. The graph makes it easy to see the sharp 
decrease in sourness perception from to 4% sucrose added, with the much 
more gradual decrease from 4 to 8% sucrose added. 




2 4 6 

Sucrose level (%) 

Fig. 12 Example of graphical form for presentation of results. 



72 



These are just a few examples of ways to present results. It might be 
necessary to try a few different ways to decide which is the best for the 
report. Remember to keep the table, chart, or graph simple and 
uncluttered. No matter in what form data are presented, properly 
tabulated or graphed data can make it easier for the researcher to 
understand the results of an experiment and can also aid in the 
communication of the results to others. 

The results should be "interpreted, compared, and contrasted" (Prell 
1976). The discussion should identify both the theoretical and practical 
significance of the results and should relate the new findings to any 
previous results, if possible. It is best to discuss the results in the same 
order as the study was carried out. 

Conclusions 

Include a final paragraph with the conclusions drawn from the study in the 
report. Keep the conclusions brief and clearly stated. Make any 
recommendations for further study at this point. 

References 

If references are used and cited, give a complete list to enable the reader to 
locate a desired citation. Refer to specific journal guidelines for the 
information required and an example of presentation format. 



73 



References 



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American Society for Testing and Materials. 1981. Guidelines for the 
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Dravnieks, A. 1985. Atlas of odor character profiles. ASTM DS 61. 
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Fisher, R.A.; Yates, F. 1974. Statistical tables for biological, agricultural and 
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74 



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637-640. 



75 



Pangborn, R.M.; Szczesniak, A.S. 1974. Effect of hydrocolloids and 
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evaluation. J. Food Sci. 28:397-403. 



76 



APPENDIXES 



77 



Statistical Chart 1 Table of random numbers, permutations of 
nine 



98119 


47634 


62128 


74824 


26316 


69967 


99242 


42293 


62781 


39637 


56945 


93661 


35153 


26837 


71926 


19563 


58873 


41611 


12194 


24228 


17798 


17455 


58857 


11764 


19452 


57975 


47815 


52523 


66834 


25245 


27285 


25299 


71782 


88679 


34114 


29662 


83196 


93516 


32777 


64843 


92581 


73375 


35341 


74918 


44949 


93188 


85428 


71742 


68486 


84787 


96479 


76491 


68563 


38259 


16396 


81659 


53578 


31322 


85352 


87336 


49537 


53434 


45961 


24814 


99952 


56378 


32381 


21148 


97297 


72848 


52498 


87383 


22131 


69919 


15466 


36866 


98794 


71675 


78536 


73495 


27778 


77622 


55159 


51263 


98581 


33164 


49769 


86257 


88255 


72928 


85426 


37137 


45775 


97913 


51435 


93913 


14312 


16975 


63226 


16691 


38586 


93122 


54874 


29581 


44112 


86349 


64849 


61622 


15644 


62331 


63645 


39681 


19752 


22217 


85847 


48893 


46597 


48774 


63557 


45963 


51428 


14254 


74566 


39789 


81433 


27339 


35951 


41886 


65455 


39863 


86891 


26531 


12772 


62737 


28622 


97744 


94399 


65615 


71385 


36396 


93289 


53491 


21397 


16212 


98532 


12463 


83527 


57693 


75743 


49661 


77747 


54358 


44124 


59213 


74862 


87515 


54246 


43585 


19779 


87859 


64959 


19174 


39259 


33113 


82151 


47924 


59642 


75834 


86518 


66168 


12838 


25974 


31147 


93998 


41141 


48426 


14937 


88522 


68628 


73483 


38217 


97468 


21345 


92374 


76989 


51436 


22266 


65776 


28685 


46622 


22565 


57564 


62716 


48346 


22575 


76356 


32234 


77979 


61291 


19143 


19222 


98313 


54127 


25553 


66127 


89656 


47931 


84577 


46781 


43718 


14871 


33813 


48879 


33229 


37769 


79698 


38599 


91485 


98384 


23448 


75582 


95118 


67862 


82865 


57997 


15656 


36185 


56864 


21884 


53946 


61484 


78366 


84292 


74722 


28657 


76693 


84137 


99632 


63148 


49438 


15937 


81498 


52455 


31229 


17273 


89719 


51741 


92313 


94375 


63931 


15454 


25941 


85392 


17996 


58885 


38247 


84138 


71165 


44722 


72575 


99477 


91117 


93856 


77347 


82872 


29147 


51457 


72341 


72394 


47919 


62519 


34731 


82898 


96724 


46815 


23931 


75785 


95794 


15923 


57213 


48683 


28624 


46578 


52168 


11983 


99488 


61586 


64968 


51183 


64763 


19332 


33622 


27299 


73355 


27846 


64569 


85256 


81471 


49461 


58617 


95634 


19211 


35232 


19449 


26624 


58256 


66356 


18461 


33139 


83758 


37622 


64593 


26875 


43544 


36979 












(continued) 



78 



Statistical Chart 1 {concluded) 



42659 


14978 


74643 


21224 


33681 


47164 


99323 


68131 


96442 


21839 


59659 


22718 


79895 


24254 


36478 


75184 


92278 


74478 


19924 


63749 


61566 


14824 


37556 


35982 


63737 


45539 


56252 


46132 


79966 


61713 


57561 


85393 


54495 


38978 


73771 


95313 


43327 


16415 


42881 


97242 


84586 


58488 


21585 


82635 


43154 


16545 


86363 


91337 


82695 


53797 


28899 


69727 


38112 


61157 


12611 


37847 


87242 


59261 


88396 


97966 


78876 


25423 


15919 


16383 


72679 


78165 


11448 


12781 


89769 


75817 


22898 


25526 


34851 


48721 


65122 


95142 


39438 


87751 


97953 


43779 


55296 


27956 


53894 


62683 


35614 


36891 


15414 


87175 


88867 


72978 


84774 


93275 


41737 


91937 


24934 


79478 


36256 


17991 


44946 


18212 


22682 


79363 


46615 


24425 


26256 


78167 


54368 


69326 


36587 


34349 


68617 


91365 


61439 


89445 


56293 


92612 


91594 


41581 


58129 


59522 


63184 


87548 


63859 


53233 


17333 


43542 


49661 


11831 


37549 


97499 


94883 


32513 


95688 


53196 


68259 


65492 


28563 


21942 


86426 


81796 


86857 


75113 


73927 


69736 


86511 


95998 


73811 


37442 


22945 


91338 


12117 


39629 


48254 


12377 


98339 


49672 


86783 


81928 


17356 


53331 


29969 


24714 


33386 


29114 


36371 


42134 


69875 


54255 


15928 


96568 


14661 


55252 


75467 


11189 


47432 


71583 


54794 


58875 


74885 


53795 


27767 


38544 


62275 


87427 


42256 


43644 


68278 


74642 


66123 


31727 


54363 


98644 


86696 


58126 


54111 


12173 


22588 


96555 


31488 


39317 


73757 


67449 


37334 


15869 


22124 


49991 


13468 


84674 


28392 


89592 


63276 


85881 


75722 


45251 


12565 


72976 


44247 


98414 


73738 


64539 


57729 


36299 


46527 


76481 


57633 


41279 


52277 


94144 


21331 


19263 


23856 


46155 


17446 


13115 


68983 


67448 


33855 


98668 


84991 


39692 


86853 


21575 


45912 


85738 


51719 


79342 


68917 


27366 


72832 


99883 


91684 


65925 


92495 


48448 


19485 


27965 


98734 


38213 


35326 


11813 


86599 


27677 


68698 


22229 


14862 


28984 


39557 


24933 


81923 


76577 


67867 


25957 


14118 


86672 


69156 


96531 


11751 


83458 


93428 


51672 


75339 


73687 


68254 


34146 


59592 


62575 


69737 


24921 


97224 


42748 


83432 


46971 


77696 


72261 


43784 


51812 


73399 


99219 


31113 


89734 


43549 


68166 


35771 


55116 


52383 


15686 


46389 


86495 


57248 


12365 


34862 


45824 


74345 


51141 


97853 



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ICNCOC0COC0c0cOcOCOc0cO'^tTj , '^'^J , Tt"^Tj < Tt<Tf'^] 



82 



Statistical Chart 5 Probability of x or more correct judgments 

in n trials of a two-out-of-five test (one-tailed, P = 0.1) a 

x 

n\ 1 2 3 4 5 6 7 8 9 10 11 12 13 

2 190 010 

3 271 028 001 

4 344 052 004 

5 410 081 009 

6 469 114 016 001 

7 522 150 026 003 

8 570 187 038 005 

9 613 225 053 008 001 

10 651 264 070 013 002 

11 686 303 090 019 003 

12 718 341 111 026 004 001 

13 746 379 134 034 006 001 

14 771 415 158 044 009 001 

15 794 451 184 056 013 002 

16 815 485 211 068 017 003 001 

17 833 518 238 083 022 005 001 

18 850 550 266 098 028 006 001 

19 865 580 295 115 035 009 002 

20 878 608 323 133 043 011 002 

21 891 635 352 152 052 014 003 001 

22 902 661 380 172 062 018 004 001 

23 911 685 408 193 073 023 006 001 

24 920 708 436 214 085 028 007 002 

25 928 729 463 236 098 033 009 002 

26 935 749 489 259 112 040 012 003 001 

27 942 767 515 282 127 047 015 004 001 

28 948 785 541 305 142 055 018 005 001 

29 953 801 565 329 158 064 022 006 002 

30 958 816 589 353 175 073 026 008 002 

31 962 830 611 376 193 083 031 010 003 001 

32 966 844 633 400 211 094 036 012 003 001 

33 969 856 654 423 230 106 042 014 004 001 

34 972 867 674 446 250 119 048 017 005 001 

35 975 878 694 469 269 132 055 020 006 002 

36 977 887 712 491 289 145 063 024 008 002 001 

37 980 896 730 514 309 160 071 027 009 003 001 

38 982 905 746 535 330 175 080 032 011 003 001 

39 984 912 762 556 350 190 089 037 013 004 001 

40 985 920 777 577 371 206 100 042 015 005 001 

41 987 926 791 597 392 223 110 048 018 006 002 

42 988 932 805 616 412 240 121 054 021 007 002 001 

43 989 938 818 635 433 257 133 061 024 009 003 001 

44 990 943 830 653 453 274 146 068 028 010 003 001 

45 991 948 841 671 473 292 159 076 032 012 004 001 

46 992 952 852 688 493 310 172 084 036 014 005 002 

47 993 956 862 704 512 329 186 093 041 016 006 002 001 

48 994 960 871 720 531 347 200 102 046 019 007 002 001 

49 994 963 880 735 550 365 215 112 052 022 008 003 001 

50 995 966 888 750 569 384 230 122 058 025 009 003 001 

a Initial decimal point has been omitted. 



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85 



Statistical Chart 8 Distribution of t 



Degrees of 




Probability of a larger value, sign i 


ignored 






freedom 




















f 


0.500 


0.400 


0.200 


0.100 


0.050 


0.025 


0.010 


0.005 


0.001 


1 


1.000 


1.376 


3.078 


6.314 


12.706 


25.452 


63.657 






2 


0.816 


1.061 


1.886 


2.920 


4.303 


6.205 


9.925 


14.089 


31.598 


3 


0.765 


0.978 


1.638 


2.353 


3.182 


4.176 


5.841 


7.453 


12.941 


4 


0.741 


0.941 


1.533 


2.132 


2.776 


3.495 


4.604 


5.598 


8.610 


5 


0.727 


0.920 


1.476 


2.015 


2.571 


3.163 


4.032 


4.773 


6.859 


6 


0.718 


0.906 


1.440 


1.943 


2.447 


2.969 


3.707 


4.317 


5.959 


7 


0.711 


0.896 


1.415 


1.895 


2.365 


2.841 


3.499 


4.029 


5.405 


8 


0.706 


0.889 


1.397 


1.860 


2.306 


2.752 


3.355 


3.832 


5.041 


9 


0.703 


0.883 


1.383 


1.833 


2.262 


2.685 


3.250 


3.690 


4.781 


10 


0.700 


0.879 


1.372 


1.812 


2.228 


2.634 


3.169 


3.581 


4.587 


11 


0.697 


0.876 


1.363 


1.796 


2.201 


2.593 


3.106 


3.497 


4.437 


12 


0.695 


0.873 


1.356 


1.782 


2.179 


2.560 


3.055 


3.428 


4.318 


13 


0.694 


0.870 


1.350 


1.771 


2.160 


2.533 


3.012 


3.372 


4.221 


14 


0.692 


0.868 


1.345 


1.761 


2.145 


2.510 


2.977 


3.326 


4.140 


15 


0.691 


0.866 


1.341 


1.753 


2.131 


2.490 


2.947 


3.286 


4.073 


16 


0.690 


0.865 


1.337 


1.746 


2.120 


2.473 


2.921 


3.252 


4.015 


17 


0.689 


0.863 


1.333 


1.740 


2.110 


2.458 


2.898 


3.222 


3.965 


18 


0.688 


0.862 


1.330 


1.734 


2.101 


2.445 


2.878 


3.197 


3.922 


19 


0.688 


0.861 


1.328 


1.729 


2.093 


2.433 


2.861 


3.174 


3.883 


20 


0.687 


0.860 


1.325 


1.725 


2.086 


2.423 


2.845 


3.153 


3.850 


21 


0.686 


0.859 


1.323 


1.721 


2.080 


2.414 


2.831 


3.135 


3.819 


22 


0.686 


0.858 


1.321 


1.717 


2.074 


2.406 


2.819 


3.119 


3.792 


23 


0.685 


0.858 


1.319 


1.714 


2.069 


2.398 


2.807 


3.104 


3.767 


24 


0.685 


0.857 


1.318 


1.711 


2.064 


2.391 


2.797 


3.090 


3.745 


25 


0.684 


0.856 


1.316 


1.708 


2.060 


2.385 


2.787 


3.078 


3.725 


26 


0.684 


0.856 


1.315 


1.706 


2.056 


2.379 


2.779 


3.067 


3.707 


27 


0.684 


0.855 


1.314 


1.703 


2.052 


2.373 


2.771 


3.056 


3.690 


28 


0.683 


0.855 


1.313 


1.701 


2.048 


2.368 


2.763 


3.047 


3.674 


29 


0.683 


0.854 


1.311 


1.699 


2.045 


2.364 


2.756 


3.038 


3.659 


30 


0.683 


0.854 


1.310 


1.697 


2.042 


2.360 


2.750 


3.030 


3.646 


35 


0.682 


0.852 


1.306 


1.690 


2.030 


2.342 


2.724 


2.996 


3.591 


40 


0.681 


0.851 


1.303 


1.684 


2.021 


2.329 


2.704 


2.971 


3.551 


45 


0.680 


0.850 


1.301 


1.680 


2.014 


2.319 


2.690 


2.952 


3.520 


50 


0.680 


0.849 


1.299 


1.676 


2.008 


2.310 


2.678 


2.937 


3.496 


55 


0.679 


0.849 


1.297 


1.673 


2.004 


2.304 


2.669 


2.925 


3.476 


60 


0.679 


0.848 


1.296 


1.671 


2.000 


2.299 


2.660 


2.915 


3.460 


70 


0.678 


0.847 


1.294 


1.667 


1.994 


2.290 


2.648 


2.899 


3.435 


80 


0.678 


0.847 


1.293 


1.665 


1.989 


2.284 


2.638 


2.887 


3.416 


90 


0.678 


0.846 


1.291 


1.662 


1.986 


2.279 


2.631 


2.878 


3.402 


100 


0.677 


0.846 


1.290 


1.661 


1.982 


2.276 


2.625 


2.871 


3.390 


120 


0.677 


0.845 


1.289 


1.658 


1.980 


2.270 


2.617 


2.860 


3.373 


oo 


0.6745 


0.8416 


1.2816 


1.6448 


1.9600 


2.2414 


2.5758 


2.8070 


3.2905 



Source: Reprinted by permission from Snedecor, G.W.; Cochran, W.G. 1989. Statistical 
methods, 8th edition. ® Iowa State University Press, Ames, Iowa. 



86 



Statistical Chart 9 Variance ratio— 5 percent points for 

distribution of F 

n 1 — degrees of freedom for numerator 

n 2 — degrees of freedom for denominator 



\ n\ 






















n>2 


1 


2 


3 


4 


5 


6 


8 


12 


24 


oo 


1 


161.4 


199.5 


215.7 


224.6 


230.2 


234.0 


238.9 


243.9 


249.0 


254.3 


2 


18.51 


19.00 


19.16 


19.25 


19.30 


19.33 


19.37 


19.41 


19.45 


19.50 


3 


10.13 


9.55 


9.28 


9.12 


9.01 


8.94 


8.84 


8.74 


8.64 


8.53 


4 


7.71 


6.94 


6.59 


6.39 


6.26 


6.16 


6.04 


5.91 


5.77 


5.63 


5 


6.61 


5.79 


5.41 


5.19 


5.05 


4.95 


4.82 


4.68 


4.53 


4.36 


6 


5.99 


5.14 


4.76 


4.53 


4.39 


4.28 


4.15 


4.00 


3.84 


3.67 


7 


5.59 


4.74 


4.35 


4.12 


3.97 


3.87 


3.73 


3.57 


3.41 


3.23 


8 


5.32 


4.46 


4.07 


3.84 


3.69 


3.58 


3.44 


3.28 


3.12 


2.93 


9 


5.12 


4.26 


3.86 


3.63 


3.48 


3.37 


3.23 


3.07 


2.90 


2.71 


10 


4.96 


4.10 


3.71 


3.48 


3.33 


3.22 


3.07 


2.91 


2.74 


2.54 


11 


4.84 


3.98 


3.59 


3.36 


3.20 


3.09 


2.95 


2.79 


2.61 


2.40 


12 


4.75 


3.88 


3.49 


3.26 


3.11 


3.00 


2.85 


2.69 


2.50 


2.30 


13 


4.67 


3.80 


3.41 


3.18 


3.02 


2.92 


2.77 


2.60 


2.42 


2.21 


14 


4.60 


3.74 


3.34 


3.11 


2.96 


2.85 


2.70 


2.53 


2.35 


2.13 


15 


4.54 


3.68 


3.29 


3.06 


2.90 


2.79 


2.64 


2.48 


2.29 


2.07 


16 


4.49 


3.63 


3.24 


3.01 


2.85 


2.74 


2.59 


2.42 


2.24 


2.01 


17 


4.45 


3.59 


3.20 


2.96 


2.81 


2.70 


2.55 


2.38 


2.19 


1.96 


18 


4.41 


3.55 


3.16 


2.93 


2.77 


2.66 


2.51 


2.34 


2.15 


1.92 


19 


4.38 


3.52 


3.13 


2.90 


2.74 


2.63 


2.48 


2.31 


2.11 


1.88 


20 


4.35 


3.49 


3.10 


2.87 


2.71 


2.60 


2.45 


2.28 


2.08 


1.84 


21 


4.32 


3.47 


3.07 


2.84 


2.68 


2.57 


2.42 


2.25 


2.05 


1.81 


22 


4.30 


3.44 


3.05 


2.82 


2.66 


2.55 


2.40 


2.23 


2.03 


1.78 


23 


4.28 


3.42 


3.03 


2.80 


2.64 


2.53 


2.38 


2.20 


2.00 


1.76 


24 


4.26 


3.40 


3.01 


2.78 


2.62 


2.51 


2.36 


2.18 


1.98 


1.73 


25 


4.24 


3.38 


2.99 


2.76 


2.60 


2.49 


2.34 


2.16 


1.96 


1.71 


26 


4.22 


3.37 


2.98 


2.74 


2.59 


2.47 


2.32 


2.15 


1.95 


1.69 


27 


4.21 


3.35 


2.96 


2.73 


2.57 


2.46 


2.30 


2.13 


1.93 


1.67 


28 


4.20 


3.34 


2.95 


2.71 


2.56 


2.44 


2.29 


2.12 


1.91 


1.65 


29 


4.18 


3.33 


2.93 


2.70 


2.54 


2.43 


2.28 


2.10 


1.90 


1.64 


30 


4.17 


3.32 


2.92 


2.69 


2.53 


2.42 


2.27 


2.09 


1.89 


1.62 


40 


4.08 


3.23 


2.84 


2.61 


2.45 


2.34 


2.18 


2.00 


1.79 


1.51 


60 


4.00 


3.15 


2.76 


2.52 


2.37 


2.25 


2.10 


1.92 


1.70 


1.39 


120 


3.92 


3.07 


2.68 


2.45 


2.29 


2.17 


2.02 


1.83 


1.61 


1.25 


oo 


3.84 


2.99 


2.60 


2.37 


2.21 


2.09 


1.94 


1.75 


1.52 


1.00 



(continued) 



87 



Statistical Chart 9 (concluded) Variance ratio— 1 percent points 

for distribution of F 

n i— degrees of freedom for numerator 

7i2— degrees of freedom for denominator 

\ n\ 
n 2 1 2 3 4 5 6 8 12 24 oo 

1 4052 4999 5403 5625 5764 5859 5981 6106 6234 6366 

2 98.49 99.00 99.17 99.25 99.30 99.33 99.36 99.42 99.46 99.50 

3 34.12 30.81 29.46 28.71 28.24 27.91 27.49 27.05 26.60 26.12 

4 21.20 18.00 16.69 15.98 15.52 15.21 14.80 14.37 13.93 13.46 



5 


16.46 


13.27 


12.06 


11.39 


10.97 


10.67 


10.29 


9.89 


9.47 


9.02 


6 


13.74 


10.92 


9.78 


9.15 


8.75 


8.47 


8.10 


7.72 


7.31 


6.88 


7 


12.25 


9.55 


8.45 


7.85 


7.46 


7.19 


6.84 


6.47 


6.07 


5.65 


8 


11.26 


8.65 


7.59 


7.01 


6.63 


6.37 


6.03 


5.67 


5.28 


4.86 


9 


10.56 


8.02 


6.99 


6.42 


6.06 


5.80 


5.47 


5.11 


4.73 


4.31 


10 


10.04 


7.56 


6.55 


5.99 


5.64 


5.39 


5.06 


4.71 


4.33 


3.91 


11 


9.65 


7.20 


6.22 


5.67 


5.32 


5.07 


4.74 


4.40 


4.02 


3.60 


12 


9.33 


6.93 


5.95 


5.41 


5.06 


4.82 


4.50 


4.16 


3.78 


3.36 


13 


9.07 


6.70 


5.74 


5.20 


4.86 


4.62 


4.30 


3.96 


3.59 


3.16 


14 


8.86 


6.51 


5.56 


5.03 


4.69 


4.46 


4.14 


3.80 


3.43 


3.00 


15 


8.68 


6.36 


5.42 


4.89 


4.56 


4.32 


4.00 


3.67 


3.29 


2.87 


16 


8.53 


6.23 


5.29 


4.77 


4.44 


4.20 


3.89 


3.55 


3.18 


2.75 


17 


8.40 


6.11 


5.18 


4.67 


4.34 


4.10 


3.79 


3.45 


3.08 


2.65 


18 


8.28 


6.01 


5.09 


4.58 


4.25 


4.01 


3.71 


3.37 


3.00 


2.57 


19 


8.18 


5.93 


5.01 


4.50 


4.17 


3.94 


3.63 


3.30 


2.92 


2.49 


20 


8.10 


5.85 


4.94 


4.43 


4.10 


3.87 


3.56 


3.23 


2.86 


2.42 


21 


8.02 


5.78 


4.87 


4.37 


4.04 


3.81 


3.51 


3.17 


2.80 


2.36 


22 


7.94 


5.72 


4.82 


4.31 


3.99 


3.76 


3.45 


3.12 


2.75 


2.31 


23 


7.88 


5.66 


4.76 


4.26 


3.94 


3.71 


3.41 


3.07 


2.70 


2.26 


24 


7.82 


5.61 


4.72 


4.22 


3.90 


3.67 


3.36 


3.03 


2.66 


2.21 


25 


7.77 


5.57 


4.68 


4.18 


3.86 


3.63 


3.32 


2.99 


2.62 


2.17 


26 


7.72 


5.53 


4.64 


4.14 


3.82 


3.59 


3.29 


2.96 


2.58 


2.13 


27 


7.68 


5.49 


4.60 


4.11 


3.78 


3.56 


3.26 


2.93 


2.55 


2.10 


28 


7.64 


5.45 


4.57 


4.07 


3.75 


3.53 


3.23 


2.90 


2.52 


2.06 


29 


7.60 


5.42 


4.54 


4.04 


3.73 


3.50 


3.20 


2.87 


2.49 


2.03 


30 


7.56 


5.39 


4.51 


4.02 


3.70 


3.47 


3.17 


2.84 


2.47 


2.01 


40 


7.31 


5.18 


4.31 


3.83 


3.51 


3.29 


2.99 


2.66 


2.29 


1.80 


60 


7.08 


4.98 


4.13 


3.65 


3.34 


3.12 


2.82 


2.50 


2.12 


1.60 


120 


6.85 


4.79 


3.95 


3.48 


3.17 


2.96 


2.66 


2.34 


1.95 


1.38 


oo 


6.64 


4.60 


3.78 


3.32 


3.02 


2.80 


2.51 


2.18 


1.79 


1.00 



Source: Table 9 is taken from Table V of Fisher and Yates: 1974 Statistical Tables for 
Biological, Agricultural and Medical Research published by Longman Group UK Ltd. 
London (previously published by Oliver and Boyd Ltd. Edinburgh) and by permission of the 
authors and publishers. 



88 



Statistical Chart 10 Table of t for one-sided Dunnett's test for 
comparing control against each of p other treatment means at 
the 5% level 





p, 


Number of treatment 


means ( 


excluding the control) 




df 


1 


2 


3 


4 


5 


6 


7 


8 


9 


5 


2.02 


2.44 


2.68 


2.85 


2.98 


3.08 


3.16 


3.24 


3.30 


6 


1.94 


2.34 


2.56 


2.71 


2.83 


2.92 


3.00 


3.07 


3.12 


7 


1.89 


2.27 


2.48 


2.62 


2.73 


2.82 


2.89 


2.95 


3.01 


8 


1.86 


2.22 


2.42 


2.55 


2.66 


2.74 


2.81 


2.87 


2.92 


9 


1.83 


2.18 


2.37 


2.50 


2.60 


2.68 


2.75 


2.81 


2.86 


10 


1.81 


2.15 


2.34 


2.47 


2.56 


2.64 


2.70 


2.76 


2.81 


11 


1.80 


2.13 


2.31 


2.44 


2.53 


2.60 


2.67 


2.72 


2.77 


12 


1.78 


2.11 


2.29 


2.41 


2.50 


2.58 


2.64 


2.69 


2.74 


13 


1.77 


2.09 


2.27 


2.39 


2.48 


2.55 


2.61 


2.66 


2.71 


14 


1.76 


2.08 


2.25 


2.37 


2.46 


2.53 


2.59 


2.64 


2.69 


15 


1.75 


2.07 


2.24 


2.36 


2.44 


2.51 


2.57 


2.62 


2.67 


16 


1.75 


2.06 


2.23 


2.34 


2.43 


2.50 


2.56 


2.61 


2.65 


17 


1.74 


2.05 


2.22 


2.33 


2.42 


2.49 


2.54 


2.59 


2.64 


18 


1.73 


2.04 


2.21 


2.32 


2.41 


2.48 


2.53 


2.58 


2.62 


19 


1.73 


2.03 


2.20 


2.31 


2.40 


2.47 


2.52 


2.57 


2.61 


20 


1.72 


2.03 


2.19 


2.30 


2.39 


2.46 


2.51 


2.56 


2.60 


24 


1.71 


2.01 


2.17 


2.28 


2.36 


2.43 


2.48 


2.53 


2.57 


30 


1.70 


1.99 


2.15 


2.25 


2.33 


2.40 


2.45 


2.50 


2.54 


40 


1.68 


1.97 


2.13 


2.23 


2.31 


2.37 


2.42 


2.47 


2.51 


60 


1.67 


1.95 


2.10 


2.21 


2.28 


2.35 


2.39 


2.44 


2.48 


120 


1.66 


1.93 


2.08 


2.18 


2.26 


2.32 


2.37 


2.41 


2.45 


oo 


1.64 


1.92 


2.06 


2.16 


2.23 


2.29 


2.34 


2.38 


2.42 



Source: Reprinted with permission from Journal of American Statistical Association— 
Dunnett, Charles W. 1955. A multiple comparison procedure for comparing several 
treatments with a control. J. Am. Stat. Assoc. 50:1096-1121. 



89 



Statistical Chart 11 Table of t for two-sided Dunnett's test for 
comparing control against each of p other treatment means at 
the 5% level 







p, Numb* 


:r of treatment means (exclud 


ing the control) 








df 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


15 


20 


5 


2.57 


3.03 


3.29 


3.48 


3.62 


3.73 


3.82 


3.90 


3.97 


4.03 


4.09 


4.14 


4.26 


4.42 


6 


2.45 


2.86 


3.10 


3.26 


3.39 


3.49 


3.57 


3.64 


3.71 


3.76 


3.81 


3.86 


3.97 


4.11 


7 


2.36 


2.75 


2.97 


3.12 


3.24 


3.33 


3.41 


3.47 


3.53 


3.58 


3.63 


3.67 


3.78 


3.91 


8 


2.31 


2.67 


2.88 


3.02 


3.13 


3.22 


3.29 


3.35 


3.41 


3.46 


3.50 


3.54 


3.64 


3.76 


9 


2.26 


2.61 


2.81 


2.95 


3.05 


3.14 


3.20 


3.26 


3.32 


3.36 


3.40 


3.44 


3.53 


3.65 


10 


2.23 


2.57 


2.76 


2.89 


2.99 


3.07 


3.14 


3.19 


3.24 


3.29 


3.33 


3.36 


3.45 


3.57 


11 


2.20 


2.53 


2.72 


2.84 


2.94 


3.02 


3.08 


3.14 


3.19 


3.23 


3.27 


3.30 


3.39 


3.50 


12 


2.18 


2.50 


2.68 


2.81 


2.90 


2.98 


3.04 


3.09 


3.14 


3.18 


3.22 


3.25 


3.34 


3.45 


13 


2.16 


2.48 


2.65 


2.78 


2.87 


2.94 


3.00 


3.06 


3.10 


3.14 


3.18 


3.21 


3.29 


3.40 


14 


2.14 


2.46 


2.63 


2.75 


2.84 


2.91 


2.97 


3.02 


3.07 


3.11 


3.14 


3.18 


3.26 


3.36 


15 


2.13 


2.44 


2.61 


2.73 


2.82 


2.89 


2.95 


3.00 


3.04 


3.08 


3.12 


3.15 


3.23 


3.33 


16 


2.12 


2.42 


2.59 


2.71 


2.80 


2.87 


2.92 


2.97 


3.02 


3.06 


3.09 


3.12 


3.20 


3.30 


17 


2.11 


2.41 


2.58 


2.69 


2.78 


2.85 


2.90 


2.95 


3.00 


3.03 


3.07 


3.10 


3.18 


3.27 


18 


2.10 


2.40 


2.56 


2.68 


2.76 


2.83 


2.89 


2.94 


2.98 


3.01 


3.05 


3.08 


3.16 


3.25 


19 


2.09 


2.39 


2.55 


2.66 


2.75 


2.81 


2.87 


2.92 


2.96 


3.00 


3.03 


3.06 


3.14 


3.23 


20 


2.09 


2.38 


2.54 


2.65 


2.73 


2.80 


2.86 


2.90 


2.95 


2.98 


3.02 


3.05 


3.12 


3.22 


24 


2.06 


2.35 


2.51 


2.61 


2.70 


2.76 


2.81 


2.86 


2.90 


2.94 


2.97 


3.00 


3.07 


3.16 


30 


2.04 


2.32 


2.47 


2.58 


2.66 


2.72 


2.77 


2.82 


2.86 


2.89 


2.92 


2.95 


3.02 


3.11 


40 


2.02 


2.29 


2.44 


2.54 


2.62 


2.68 


2.73 


2.77 


2.81 


2.85 


2.87 


2.90 


2.97 


3.06 


60 


2.00 


2.27 


2.41 


2.51 


2.58 


2.64 


2.69 


2.73 


2.77 


2.80 


2.83 


2.86 


2.92 


3.00 


120 


1.98 


2.24 


2.38 


2.47 


2.55 


2.60 


2.65 


2.69 


2.73 


2.76 


2.79 


2.81 


2.87 


2.95 


oo 


1.96 


2.21 


2.35 


2.44 


2.51 


2.57 


2.61 


2.65 


2.69 


2.72 


2.74 


2.77 


2.83 


2.91 



Source: Reproduced from Dunnett, C.W. 1964. New tables for multiple comparisons with a 
control. Biometrics 20:482-491; with permission of The Biometric Society. 



90 





CONVERSION FACTORS 




Multiply an imperial number by the conversion factor given to get its 


metric equivalent. 








Divide a metric number by the conversion factor given to get its equivalent 


in imperial units. 


Approximate 






Imperial units 


conversion factor 


Metric units 


Length 








inch 


25 


millimetre 


(mm) 


foot 


30 


centimetre 


(cm) 


yard 


0.9 


metre 


(m) 


mile 


1.6 


kilometre 


(km) 


Area 








square inch 


6.5 


square centimetre 


(cm 2 ) 


square foot 


0.09 


square metre 


(m 2 ) 


square yard 


0.836 


square metre 


(m 2 ) 


square mile 


259 


hectare 


(ha) 


acre 


0.40 


hectare 


(ha) 


Volume 








cubic inch 


16 


cubic centimetre 


(cm*, mL, cc) 


cubic foot 


28 


cubic decimetre 


(dm') 


cubic yard 


0.8 


cubic metre 


(m s ) 


fluid ounce 


28 


millilitre 


(mL) 


pint 


0.57 


litre 


(L) 


quart 


1.1 


litre 


(L) 


gallon (Imp.) 


4.5 


litre 


(L) 


gallon (U.S.) 


3.8 


litre 


(L) 


Weight 








ounce 


28 


gram 


(g) 


pound 


0.45 


kilogram 


(kg) 


short ton (2000 lb) 


0.9 


tonne 


(t) 


Pressure 








pounds per square inch 


6.9 


kilopascal 


(kPa) 


Power 








horsepower 


746 


watt 


(W) 




0.75 


kilowatt 


(kW) 


Speed 








feet per second 


0.30 


metres per second 


(m/s) 


miles per hour 


1.6 


kilometres per hour 


(km/h) 


Agriculture 








gallons per acre 


11.23 


litres per hectare 


(L/ha) 


quarts per acre 


2.8 


litres per hectare 


(L/ha) 


pints per acre 


1.4 


litres per hectare 


(L/ha) 


fluid ounces per acre 


70 


milliltres per hectare 


(mL/ha) 


tons per acre 


2.24 


tonnes per hectare 


(t/ha) 


pounds per acre 


1.12 


kilograms per hectare 


(kg/ha) 


ounces per acre 


70 


grams per hectare 


(g/ha) 


plants per acre 


2.47 


plants per hectare 




Temperature 








degrees Fahrenheit 


CF-32) x 


0.56 = *C degrees 






or 'F = 1.8 (°C) + 32 Celsius 


CC) 



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